<!doctype html>
<html lang="en-US">
<head>
	<meta charset="UTF-8" />
	<meta name="viewport" content="width=device-width, initial-scale=1" />
	<link rel="profile" href="https://gmpg.org/xfn/11" />
	<title>Calculus &#8211; Solved Problems</title>
<meta name='robots' content='max-image-preview:large' />
<link rel='dns-prefetch' href='//secure.gravatar.com' />
<link rel='dns-prefetch' href='//stats.wp.com' />
<link rel='dns-prefetch' href='//v0.wordpress.com' />
<link rel="alternate" type="application/rss+xml" title="Solved Problems &raquo; Feed" href="https://www.solved-problems.com/feed/" />
<link rel="alternate" type="application/rss+xml" title="Solved Problems &raquo; Comments Feed" href="https://www.solved-problems.com/comments/feed/" />
<link rel="alternate" type="application/rss+xml" title="Solved Problems &raquo; Calculus Category Feed" href="https://www.solved-problems.com/topic/calculus/feed/" />
<script>
window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/14.0.0\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/14.0.0\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/www.solved-problems.com\/wp-includes\/js\/wp-emoji-release.min.js?ver=6.2.2"}};
/*! This file is auto-generated */
!function(e,a,t){var n,r,o,i=a.createElement("canvas"),p=i.getContext&&i.getContext("2d");function s(e,t){p.clearRect(0,0,i.width,i.height),p.fillText(e,0,0);e=i.toDataURL();return p.clearRect(0,0,i.width,i.height),p.fillText(t,0,0),e===i.toDataURL()}function c(e){var t=a.createElement("script");t.src=e,t.defer=t.type="text/javascript",a.getElementsByTagName("head")[0].appendChild(t)}for(o=Array("flag","emoji"),t.supports={everything:!0,everythingExceptFlag:!0},r=0;r<o.length;r++)t.supports[o[r]]=function(e){if(p&&p.fillText)switch(p.textBaseline="top",p.font="600 32px Arial",e){case"flag":return s("\ud83c\udff3\ufe0f\u200d\u26a7\ufe0f","\ud83c\udff3\ufe0f\u200b\u26a7\ufe0f")?!1:!s("\ud83c\uddfa\ud83c\uddf3","\ud83c\uddfa\u200b\ud83c\uddf3")&&!s("\ud83c\udff4\udb40\udc67\udb40\udc62\udb40\udc65\udb40\udc6e\udb40\udc67\udb40\udc7f","\ud83c\udff4\u200b\udb40\udc67\u200b\udb40\udc62\u200b\udb40\udc65\u200b\udb40\udc6e\u200b\udb40\udc67\u200b\udb40\udc7f");case"emoji":return!s("\ud83e\udef1\ud83c\udffb\u200d\ud83e\udef2\ud83c\udfff","\ud83e\udef1\ud83c\udffb\u200b\ud83e\udef2\ud83c\udfff")}return!1}(o[r]),t.supports.everything=t.supports.everything&&t.supports[o[r]],"flag"!==o[r]&&(t.supports.everythingExceptFlag=t.supports.everythingExceptFlag&&t.supports[o[r]]);t.supports.everythingExceptFlag=t.supports.everythingExceptFlag&&!t.supports.flag,t.DOMReady=!1,t.readyCallback=function(){t.DOMReady=!0},t.supports.everything||(n=function(){t.readyCallback()},a.addEventListener?(a.addEventListener("DOMContentLoaded",n,!1),e.addEventListener("load",n,!1)):(e.attachEvent("onload",n),a.attachEvent("onreadystatechange",function(){"complete"===a.readyState&&t.readyCallback()})),(e=t.source||{}).concatemoji?c(e.concatemoji):e.wpemoji&&e.twemoji&&(c(e.twemoji),c(e.wpemoji)))}(window,document,window._wpemojiSettings);
</script>
<style>
img.wp-smiley,
img.emoji {
	display: inline !important;
	border: none !important;
	box-shadow: none !important;
	height: 1em !important;
	width: 1em !important;
	margin: 0 0.07em !important;
	vertical-align: -0.1em !important;
	background: none !important;
	padding: 0 !important;
}
</style>
	<link rel='stylesheet' id='wp-quicklatex-format-css' href='https://www.solved-problems.com/wp-content/plugins/wp-quicklatex/css/quicklatex-format.css?ver=6.2.2' media='all' />
<link rel='stylesheet' id='twentynineteen-jetpack-css' href='https://www.solved-problems.com/wp-content/plugins/jetpack/modules/theme-tools/compat/twentynineteen.css?ver=12.3' media='all' />
<link rel='stylesheet' id='wp-block-library-css' href='https://www.solved-problems.com/wp-includes/css/dist/block-library/style.min.css?ver=6.2.2' media='all' />
<style id='wp-block-library-inline-css'>
.has-text-align-justify{text-align:justify;}
</style>
<style id='wp-block-library-theme-inline-css'>
.wp-block-audio figcaption{color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-audio figcaption{color:hsla(0,0%,100%,.65)}.wp-block-audio{margin:0 0 1em}.wp-block-code{border:1px solid #ccc;border-radius:4px;font-family:Menlo,Consolas,monaco,monospace;padding:.8em 1em}.wp-block-embed figcaption{color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-embed figcaption{color:hsla(0,0%,100%,.65)}.wp-block-embed{margin:0 0 1em}.blocks-gallery-caption{color:#555;font-size:13px;text-align:center}.is-dark-theme .blocks-gallery-caption{color:hsla(0,0%,100%,.65)}.wp-block-image figcaption{color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-image figcaption{color:hsla(0,0%,100%,.65)}.wp-block-image{margin:0 0 1em}.wp-block-pullquote{border-bottom:4px solid;border-top:4px solid;color:currentColor;margin-bottom:1.75em}.wp-block-pullquote cite,.wp-block-pullquote footer,.wp-block-pullquote__citation{color:currentColor;font-size:.8125em;font-style:normal;text-transform:uppercase}.wp-block-quote{border-left:.25em solid;margin:0 0 1.75em;padding-left:1em}.wp-block-quote cite,.wp-block-quote footer{color:currentColor;font-size:.8125em;font-style:normal;position:relative}.wp-block-quote.has-text-align-right{border-left:none;border-right:.25em solid;padding-left:0;padding-right:1em}.wp-block-quote.has-text-align-center{border:none;padding-left:0}.wp-block-quote.is-large,.wp-block-quote.is-style-large,.wp-block-quote.is-style-plain{border:none}.wp-block-search .wp-block-search__label{font-weight:700}.wp-block-search__button{border:1px solid #ccc;padding:.375em .625em}:where(.wp-block-group.has-background){padding:1.25em 2.375em}.wp-block-separator.has-css-opacity{opacity:.4}.wp-block-separator{border:none;border-bottom:2px solid;margin-left:auto;margin-right:auto}.wp-block-separator.has-alpha-channel-opacity{opacity:1}.wp-block-separator:not(.is-style-wide):not(.is-style-dots){width:100px}.wp-block-separator.has-background:not(.is-style-dots){border-bottom:none;height:1px}.wp-block-separator.has-background:not(.is-style-wide):not(.is-style-dots){height:2px}.wp-block-table{margin:0 0 1em}.wp-block-table td,.wp-block-table th{word-break:normal}.wp-block-table figcaption{color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-table figcaption{color:hsla(0,0%,100%,.65)}.wp-block-video figcaption{color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-video figcaption{color:hsla(0,0%,100%,.65)}.wp-block-video{margin:0 0 1em}.wp-block-template-part.has-background{margin-bottom:0;margin-top:0;padding:1.25em 2.375em}
</style>
<link rel='stylesheet' id='jetpack-videopress-video-block-view-css' href='https://www.solved-problems.com/wp-content/plugins/jetpack/jetpack_vendor/automattic/jetpack-videopress/build/block-editor/blocks/video/view.css?minify=false&#038;ver=34ae973733627b74a14e' media='all' />
<link rel='stylesheet' id='mediaelement-css' href='https://www.solved-problems.com/wp-includes/js/mediaelement/mediaelementplayer-legacy.min.css?ver=4.2.17' media='all' />
<link rel='stylesheet' id='wp-mediaelement-css' href='https://www.solved-problems.com/wp-includes/js/mediaelement/wp-mediaelement.min.css?ver=6.2.2' media='all' />
<link rel='stylesheet' id='classic-theme-styles-css' href='https://www.solved-problems.com/wp-includes/css/classic-themes.min.css?ver=6.2.2' media='all' />
<style id='global-styles-inline-css'>
body{--wp--preset--color--black: #000000;--wp--preset--color--cyan-bluish-gray: #abb8c3;--wp--preset--color--white: #FFF;--wp--preset--color--pale-pink: #f78da7;--wp--preset--color--vivid-red: #cf2e2e;--wp--preset--color--luminous-vivid-orange: #ff6900;--wp--preset--color--luminous-vivid-amber: #fcb900;--wp--preset--color--light-green-cyan: #7bdcb5;--wp--preset--color--vivid-green-cyan: #00d084;--wp--preset--color--pale-cyan-blue: #8ed1fc;--wp--preset--color--vivid-cyan-blue: #0693e3;--wp--preset--color--vivid-purple: #9b51e0;--wp--preset--color--primary: #0073a8;--wp--preset--color--secondary: #005075;--wp--preset--color--dark-gray: #111;--wp--preset--color--light-gray: #767676;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple: linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan: linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange: linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red: linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray: linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum: linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple: linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux: linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk: linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean: linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass: linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight: linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--duotone--dark-grayscale: url('#wp-duotone-dark-grayscale');--wp--preset--duotone--grayscale: url('#wp-duotone-grayscale');--wp--preset--duotone--purple-yellow: url('#wp-duotone-purple-yellow');--wp--preset--duotone--blue-red: url('#wp-duotone-blue-red');--wp--preset--duotone--midnight: url('#wp-duotone-midnight');--wp--preset--duotone--magenta-yellow: url('#wp-duotone-magenta-yellow');--wp--preset--duotone--purple-green: url('#wp-duotone-purple-green');--wp--preset--duotone--blue-orange: url('#wp-duotone-blue-orange');--wp--preset--font-size--small: 19.5px;--wp--preset--font-size--medium: 20px;--wp--preset--font-size--large: 36.5px;--wp--preset--font-size--x-large: 42px;--wp--preset--font-size--normal: 22px;--wp--preset--font-size--huge: 49.5px;--wp--preset--spacing--20: 0.44rem;--wp--preset--spacing--30: 0.67rem;--wp--preset--spacing--40: 1rem;--wp--preset--spacing--50: 1.5rem;--wp--preset--spacing--60: 2.25rem;--wp--preset--spacing--70: 3.38rem;--wp--preset--spacing--80: 5.06rem;--wp--preset--shadow--natural: 6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep: 12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp: 6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined: 6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp: 6px 6px 0px rgba(0, 0, 0, 1);}:where(.is-layout-flex){gap: 0.5em;}body .is-layout-flow > .alignleft{float: left;margin-inline-start: 0;margin-inline-end: 2em;}body .is-layout-flow > .alignright{float: right;margin-inline-start: 2em;margin-inline-end: 0;}body .is-layout-flow > .aligncenter{margin-left: auto !important;margin-right: auto !important;}body .is-layout-constrained > .alignleft{float: left;margin-inline-start: 0;margin-inline-end: 2em;}body .is-layout-constrained > .alignright{float: right;margin-inline-start: 2em;margin-inline-end: 0;}body .is-layout-constrained > .aligncenter{margin-left: auto !important;margin-right: auto !important;}body .is-layout-constrained > :where(:not(.alignleft):not(.alignright):not(.alignfull)){max-width: var(--wp--style--global--content-size);margin-left: auto !important;margin-right: auto !important;}body .is-layout-constrained > .alignwide{max-width: var(--wp--style--global--wide-size);}body .is-layout-flex{display: flex;}body .is-layout-flex{flex-wrap: wrap;align-items: center;}body .is-layout-flex > *{margin: 0;}:where(.wp-block-columns.is-layout-flex){gap: 2em;}.has-black-color{color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color: var(--wp--preset--color--white) !important;}.has-pale-pink-color{color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color: var(--wp--preset--color--vivid-purple) !important;}.has-black-background-color{background-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color: var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color: var(--wp--preset--color--vivid-purple) !important;}.has-black-border-color{border-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color: var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color: var(--wp--preset--color--vivid-purple) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background: var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background: var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background: var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background: var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background: var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background: var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background: var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background: var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background: var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background: var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size: var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size: var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size: var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size: var(--wp--preset--font-size--x-large) !important;}
.wp-block-navigation a:where(:not(.wp-element-button)){color: inherit;}
:where(.wp-block-columns.is-layout-flex){gap: 2em;}
.wp-block-pullquote{font-size: 1.5em;line-height: 1.6;}
</style>
<link rel='stylesheet' id='twentynineteen-style-css' href='https://www.solved-problems.com/wp-content/themes/twentynineteen/style.css?ver=2.5' media='all' />
<link rel='stylesheet' id='twentynineteen-print-style-css' href='https://www.solved-problems.com/wp-content/themes/twentynineteen/print.css?ver=2.5' media='print' />
<link rel='stylesheet' id='jetpack_css-css' href='https://www.solved-problems.com/wp-content/plugins/jetpack/css/jetpack.css?ver=12.3' media='all' />
<script src='https://www.solved-problems.com/wp-includes/js/jquery/jquery.min.js?ver=3.6.4' id='jquery-core-js'></script>
<script src='https://www.solved-problems.com/wp-includes/js/jquery/jquery-migrate.min.js?ver=3.4.0' id='jquery-migrate-js'></script>
<script src='https://www.solved-problems.com/wp-content/plugins/wp-quicklatex/js/wp-quicklatex-frontend.js?ver=1.0' id='wp-quicklatex-frontend-js'></script>
<link rel="https://api.w.org/" href="https://www.solved-problems.com/wp-json/" /><link rel="alternate" type="application/json" href="https://www.solved-problems.com/wp-json/wp/v2/categories/123" /><link rel="EditURI" type="application/rsd+xml" title="RSD" href="https://www.solved-problems.com/xmlrpc.php?rsd" />
<link rel="wlwmanifest" type="application/wlwmanifest+xml" href="https://www.solved-problems.com/wp-includes/wlwmanifest.xml" />
<meta name="generator" content="WordPress 6.2.2" />
	<style>
	.post-1562 .display-posts-listing.image-right .listing-item {
		overflow: hidden; 
		margin-bottom: 32px;
		width: 100%;
	}

	.post-1562 .display-posts-listing.image-right .image {
		float: right;
		margin: 0 16px 0 0;
	}

	.post-1562 .display-posts-listing.image-right .title {
		display: block;
	}

	.post-1562 .display-posts-listing.image-right .excerpt-dash { 
		display: none; 
	}
	.post-1562 .listing-item a{
		font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", "Roboto", "Oxygen", "Ubuntu", "Cantarell", "Fira Sans", "Droid Sans", "Helvetica Neue", sans-serif;
		font-weight: bold;
	}							
	</style>
	<style>img#wpstats{display:none}</style>
		<style>.recentcomments a{display:inline !important;padding:0 !important;margin:0 !important;}</style>
<!-- Jetpack Open Graph Tags -->
<meta property="og:type" content="website" />
<meta property="og:title" content="Calculus &#8211; Solved Problems" />
<meta property="og:url" content="https://www.solved-problems.com/topic/calculus/" />
<meta property="og:description" content="Solved Problems in Calculus" />
<meta property="og:site_name" content="Solved Problems" />
<meta property="og:image" content="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4-1.png" />
<meta property="og:image:width" content="512" />
<meta property="og:image:height" content="512" />
<meta property="og:image:alt" content="" />
<meta property="og:locale" content="en_US" />

<!-- End Jetpack Open Graph Tags -->
<link rel="icon" href="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4-1-32x32.png" sizes="32x32" />
<link rel="icon" href="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4-1-192x192.png" sizes="192x192" />
<link rel="apple-touch-icon" href="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4-1-180x180.png" />
<meta name="msapplication-TileImage" content="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4-1-270x270.png" />
</head>

<body class="archive category category-calculus category-123 wp-custom-logo wp-embed-responsive hfeed image-filters-enabled">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-dark-grayscale"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0 0.49803921568627" /><feFuncG type="table" tableValues="0 0.49803921568627" /><feFuncB type="table" tableValues="0 0.49803921568627" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-grayscale"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0 1" /><feFuncG type="table" tableValues="0 1" /><feFuncB type="table" tableValues="0 1" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-purple-yellow"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0.54901960784314 0.98823529411765" /><feFuncG type="table" tableValues="0 1" /><feFuncB type="table" tableValues="0.71764705882353 0.25490196078431" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-blue-red"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0 1" /><feFuncG type="table" tableValues="0 0.27843137254902" /><feFuncB type="table" tableValues="0.5921568627451 0.27843137254902" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-midnight"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0 0" /><feFuncG type="table" tableValues="0 0.64705882352941" /><feFuncB type="table" tableValues="0 1" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-magenta-yellow"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0.78039215686275 1" /><feFuncG type="table" tableValues="0 0.94901960784314" /><feFuncB type="table" tableValues="0.35294117647059 0.47058823529412" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-purple-green"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0.65098039215686 0.40392156862745" /><feFuncG type="table" tableValues="0 1" /><feFuncB type="table" tableValues="0.44705882352941 0.4" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 0 0" width="0" height="0" focusable="false" role="none" style="visibility: hidden; position: absolute; left: -9999px; overflow: hidden;" ><defs><filter id="wp-duotone-blue-orange"><feColorMatrix color-interpolation-filters="sRGB" type="matrix" values=" .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 .299 .587 .114 0 0 " /><feComponentTransfer color-interpolation-filters="sRGB" ><feFuncR type="table" tableValues="0.098039215686275 1" /><feFuncG type="table" tableValues="0 0.66274509803922" /><feFuncB type="table" tableValues="0.84705882352941 0.41960784313725" /><feFuncA type="table" tableValues="1 1" /></feComponentTransfer><feComposite in2="SourceGraphic" operator="in" /></filter></defs></svg><div id="page" class="site">
	<a class="skip-link screen-reader-text" href="#content">
		Skip to content	</a>

		<header id="masthead" class="site-header">

			<div class="site-branding-container">
				<div class="site-branding">

			<div class="site-logo"><a href="https://www.solved-problems.com/" class="custom-logo-link" rel="home"><img width="190" height="190" src="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4.png" class="custom-logo" alt="Solved Problems" decoding="async" srcset="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4.png 190w, https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4-150x150.png 150w" sizes="(max-width: 34.9rem) calc(100vw - 2rem), (max-width: 53rem) calc(8 * (100vw / 12)), (min-width: 53rem) calc(6 * (100vw / 12)), 100vw" data-attachment-id="1610" data-permalink="https://www.solved-problems.com/cropped-icon4-png/" data-orig-file="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4.png" data-orig-size="190,190" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="cropped-icon4.png" data-image-description="&lt;p&gt;http://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4.png&lt;/p&gt;
" data-image-caption="" data-medium-file="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4.png" data-large-file="https://www.solved-problems.com/wp-content/uploads/2019/08/cropped-icon4.png" /></a></div>
								<p class="site-title"><a href="https://www.solved-problems.com/" rel="home">Solved Problems</a></p>
			
				<p class="site-description">
				A Source of Free Solved Problems			</p>
				<nav id="site-navigation" class="main-navigation" aria-label="Top Menu">
			<div class="menu-new-container"><ul id="menu-new" class="main-menu"><li id="menu-item-1164" class="menu-item menu-item-type-taxonomy menu-item-object-category current-menu-item menu-item-has-children menu-item-1164"><a href="https://www.solved-problems.com/topic/calculus/" aria-current="page" aria-haspopup="true" aria-expanded="false">Calculus</a><button class="submenu-expand" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.41 8.59L12 13.17l4.59-4.58L18 10l-6 6-6-6 1.41-1.41z"></path><path fill="none" d="M0 0h24v24H0V0z"></path></svg></button>
<ul class="sub-menu">
	<li id="menu-item--1" class="mobile-parent-nav-menu-item menu-item--1"><button class="menu-item-link-return" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M15.41 7.41L14 6l-6 6 6 6 1.41-1.41L10.83 12z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg>Calculus</button></li>
	<li id="menu-item-1165" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1165"><a href="https://www.solved-problems.com/topic/calculus/derivative/">Derivative</a></li>
	<li id="menu-item-1166" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1166"><a href="https://www.solved-problems.com/topic/calculus/integral/">Integral</a></li>
	<li id="menu-item-1167" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1167"><a href="https://www.solved-problems.com/topic/calculus/limits/">Limits</a></li>
	<li id="menu-item-1168" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1168"><a href="https://www.solved-problems.com/topic/calculus/precalculus/">Precalculus</a></li>
</ul>
</li>
<li id="menu-item-1169" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-has-children menu-item-1169"><a href="https://www.solved-problems.com/topic/circuits/" aria-haspopup="true" aria-expanded="false">Electrical Circuits</a><button class="submenu-expand" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.41 8.59L12 13.17l4.59-4.58L18 10l-6 6-6-6 1.41-1.41z"></path><path fill="none" d="M0 0h24v24H0V0z"></path></svg></button>
<ul class="sub-menu">
	<li id="menu-item--2" class="mobile-parent-nav-menu-item menu-item--2"><button class="menu-item-link-return" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M15.41 7.41L14 6l-6 6 6 6 1.41-1.41L10.83 12z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg>Electrical Circuits</button></li>
	<li id="menu-item-1170" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1170"><a href="https://www.solved-problems.com/topic/circuits/circuits-articles/">Articles</a></li>
	<li id="menu-item-1171" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-has-children menu-item-1171"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/" aria-haspopup="true" aria-expanded="false">Problems</a><button class="submenu-expand" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.41 8.59L12 13.17l4.59-4.58L18 10l-6 6-6-6 1.41-1.41z"></path><path fill="none" d="M0 0h24v24H0V0z"></path></svg></button>
	<ul class="sub-menu">
		<li id="menu-item--3" class="mobile-parent-nav-menu-item menu-item--3"><button class="menu-item-link-return" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M15.41 7.41L14 6l-6 6 6 6 1.41-1.41L10.83 12z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg>Problems</button></li>
		<li id="menu-item-1172" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1172"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/basic-concepts/">Basic Concepts</a></li>
		<li id="menu-item-1173" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1173"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/capacitors-and-inductors/">Capacitors and Inductors</a></li>
		<li id="menu-item-1174" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1174"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/resistive-circuits/">Resistive Circuits</a></li>
	</ul>
</li>
</ul>
</li>
<li id="menu-item-1422" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-has-children menu-item-1422"><a href="https://www.solved-problems.com/topic/control-systems/" aria-haspopup="true" aria-expanded="false">Control Systems</a><button class="submenu-expand" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.41 8.59L12 13.17l4.59-4.58L18 10l-6 6-6-6 1.41-1.41z"></path><path fill="none" d="M0 0h24v24H0V0z"></path></svg></button>
<ul class="sub-menu">
	<li id="menu-item--4" class="mobile-parent-nav-menu-item menu-item--4"><button class="menu-item-link-return" tabindex="-1"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M15.41 7.41L14 6l-6 6 6 6 1.41-1.41L10.83 12z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg>Control Systems</button></li>
	<li id="menu-item-1423" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1423"><a href="https://www.solved-problems.com/topic/control-systems/stability/">Stability</a></li>
</ul>
</li>
<li id="menu-item-1182" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-1182"><a href="http://www.solved-problems.com/circuits/circuits-articles/696/nodal-analysis/">Nodal Analysis eBook</a></li>
<li id="menu-item-1383" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-1383"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-contests/">Contests</a></li>
</ul></div>
			<div class="main-menu-more">
				<ul class="main-menu">
					<li class="menu-item menu-item-has-children">
						<button class="submenu-expand main-menu-more-toggle is-empty" tabindex="-1"
							aria-label="More" aria-haspopup="true" aria-expanded="false"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg"><g fill="none" fill-rule="evenodd"><path d="M0 0h24v24H0z"/><path fill="currentColor" fill-rule="nonzero" d="M12 2c5.52 0 10 4.48 10 10s-4.48 10-10 10S2 17.52 2 12 6.48 2 12 2zM6 14a2 2 0 1 0 0-4 2 2 0 0 0 0 4zm6 0a2 2 0 1 0 0-4 2 2 0 0 0 0 4zm6 0a2 2 0 1 0 0-4 2 2 0 0 0 0 4z"/></g></svg>
						</button>
						<ul class="sub-menu hidden-links">
							<li class="mobile-parent-nav-menu-item">
								<button class="menu-item-link-return"><svg class="svg-icon" width="24" height="24" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M15.41 7.41L14 6l-6 6 6 6 1.41-1.41L10.83 12z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg>Back
								</button>
							</li>
						</ul>
					</li>
				</ul>
			</div>		</nav><!-- #site-navigation -->
		</div><!-- .site-branding -->
			</div><!-- .site-branding-container -->

					</header><!-- #masthead -->

	<div id="content" class="site-content">

	<div id="primary" class="content-area">
		<main id="main" class="site-main">

		
			<header class="page-header">
				<h1 class="page-title">Category Archives: <span class="page-description">Calculus</span></h1>			</header><!-- .page-header -->

			
<article id="post-829" class="post-829 post type-post status-publish format-standard hentry category-precalculus tag-quadratic tag-quadratic-equations tag-solving-equations tag-solving-linear-equations tag-square-roots entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/precalculus/829/solving-quadratic-equations-ii-square-roots/" rel="bookmark">Solving Quadratic Equations II: Taking Square Roots</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Solving quadratic equations by taking the square root of both sides of the equation is explained. Some examples are provided to show the method step by step.</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/829/solving-quadratic-equations-ii-square-roots/" rel="bookmark"><time class="entry-date published updated" datetime="2010-07-31T22:28:59+00:00">July 31, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/precalculus/" rel="category tag">Precalculus</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/quadratic/" rel="tag">Quadratic</a>, <a href="https://www.solved-problems.com/tag/quadratic-equations/" rel="tag">Quadratic Equations</a>, <a href="https://www.solved-problems.com/tag/solving-equations/" rel="tag">solving equations</a>, <a href="https://www.solved-problems.com/tag/solving-linear-equations/" rel="tag">solving linear equations</a>, <a href="https://www.solved-problems.com/tag/square-roots/" rel="tag">Square Roots</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/829/solving-quadratic-equations-ii-square-roots/#comments">2 Comments<span class="screen-reader-text"> on Solving Quadratic Equations II: Taking Square Roots</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-829 -->

<article id="post-814" class="post-814 post type-post status-publish format-standard hentry category-precalculus tag-factoring tag-factors tag-quadratic tag-quadratic-equations tag-solving-equations entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/precalculus/814/solving-quadratic-equations-i-factoring-grouping/" rel="bookmark">Solving Quadratic Equations I: Factoring (Grouping)</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Solving quadratic equations by factoring is explained with some examples. Two methods are introduced to factorize quadratic equations. Other methods of solving quadratic equations are also addressed.</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/814/solving-quadratic-equations-i-factoring-grouping/" rel="bookmark"><time class="entry-date published" datetime="2010-07-15T06:55:50+00:00">July 15, 2010</time><time class="updated" datetime="2013-09-25T00:11:03+00:00">September 25, 2013</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/precalculus/" rel="category tag">Precalculus</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/factoring/" rel="tag">Factoring</a>, <a href="https://www.solved-problems.com/tag/factors/" rel="tag">Factors</a>, <a href="https://www.solved-problems.com/tag/quadratic/" rel="tag">Quadratic</a>, <a href="https://www.solved-problems.com/tag/quadratic-equations/" rel="tag">Quadratic Equations</a>, <a href="https://www.solved-problems.com/tag/solving-equations/" rel="tag">solving equations</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/814/solving-quadratic-equations-i-factoring-grouping/#comments">2 Comments<span class="screen-reader-text"> on Solving Quadratic Equations I: Factoring (Grouping)</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-814 -->

<article id="post-790" class="post-790 post type-post status-publish format-standard hentry category-precalculus tag-radical tag-radical-equations tag-solving-equations entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/precalculus/790/solving-equations-ii/" rel="bookmark">Solving Equations II: Radical Equations</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>This article explains the process of solving equations with radicals. Solving radical equations is performed by isolating radicals and raising both sides to a power equal to the index of the radicals one by one. The method is explained and ten examples are solved to illustrate solving equations with radicals.</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/790/solving-equations-ii/" rel="bookmark"><time class="entry-date published updated" datetime="2010-07-10T21:25:13+00:00">July 10, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/precalculus/" rel="category tag">Precalculus</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/radical/" rel="tag">Radical</a>, <a href="https://www.solved-problems.com/tag/radical-equations/" rel="tag">Radical Equations</a>, <a href="https://www.solved-problems.com/tag/solving-equations/" rel="tag">solving equations</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/790/solving-equations-ii/#comments">2 Comments<span class="screen-reader-text"> on Solving Equations II: Radical Equations</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-790 -->

<article id="post-776" class="post-776 post type-post status-publish format-standard hentry category-precalculus tag-isolation tag-solving-equations tag-solving-linear-equations entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/precalculus/776/solving-equations-i/" rel="bookmark">Solving Equations I: Linear Equations</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>This article explains the process of solving equations of linear form. Solving linear equations is performed by isolating the unknown variable. Two methods are introduced to fulfill isolation. The article also contains ten examples to illustrate solving equations.</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/776/solving-equations-i/" rel="bookmark"><time class="entry-date published updated" datetime="2010-07-10T01:06:56+00:00">July 10, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/precalculus/" rel="category tag">Precalculus</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/isolation/" rel="tag">isolation</a>, <a href="https://www.solved-problems.com/tag/solving-equations/" rel="tag">solving equations</a>, <a href="https://www.solved-problems.com/tag/solving-linear-equations/" rel="tag">solving linear equations</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/776/solving-equations-i/#respond">Leave a comment<span class="screen-reader-text"> on Solving Equations I: Linear Equations</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-776 -->

<article id="post-241" class="post-241 post type-post status-publish format-standard hentry category-derivative tag-chain-rule tag-differentiation-formula entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/derivative/241/problem-2-11/" rel="bookmark">Problem 2-11: Differentiating by Chain Rule</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Differentiating (1+sqrt(x))^8 by the chain rule.  Determining individual components of the chain rule.</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/derivative/241/problem-2-11/" rel="bookmark"><time class="entry-date published updated" datetime="2010-04-11T03:22:41+00:00">April 11, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/derivative/" rel="category tag">Derivative</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/chain-rule/" rel="tag">chain rule</a>, <a href="https://www.solved-problems.com/tag/differentiation-formula/" rel="tag">Differentiation Formula</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/derivative/241/problem-2-11/#comments">1 Comment<span class="screen-reader-text"> on Problem 2-11: Differentiating by Chain Rule</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-241 -->

<article id="post-234" class="post-234 post type-post status-publish format-standard hentry category-derivative tag-differentiation-formula tag-division tag-multiplication entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/derivative/234/problem-2-10/" rel="bookmark">Problem 2-10: Diffrentiating</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Diffrentiating f(x)= (1-2x^2)/(1+x+x^2) and f(x)= (1-2x^2)(1+x+x^2)</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/derivative/234/problem-2-10/" rel="bookmark"><time class="entry-date published updated" datetime="2010-04-11T02:47:37+00:00">April 11, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/derivative/" rel="category tag">Derivative</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/differentiation-formula/" rel="tag">Differentiation Formula</a>, <a href="https://www.solved-problems.com/tag/division/" rel="tag">division</a>, <a href="https://www.solved-problems.com/tag/multiplication/" rel="tag">multiplication</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/derivative/234/problem-2-10/#respond">Leave a comment<span class="screen-reader-text"> on Problem 2-10: Diffrentiating</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-234 -->

<article id="post-215" class="post-215 post type-post status-publish format-standard hentry category-derivative tag-polynomial-function tag-rational-function entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/derivative/215/problem-2-9/" rel="bookmark">Problem 2-9: Differentiating Polynomial and Rational Functions</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Differentiating f(x)= 1+ 2x, f(x)= 1 &#8211; 2x + 2x^2, f(x)= 1- x^2 +1/x and f(x)= 1 &#8211; x +1/(1-x)</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/derivative/215/problem-2-9/" rel="bookmark"><time class="entry-date published updated" datetime="2010-04-11T01:57:33+00:00">April 11, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/derivative/" rel="category tag">Derivative</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/polynomial-function/" rel="tag">polynomial function</a>, <a href="https://www.solved-problems.com/tag/rational-function/" rel="tag">rational function</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/derivative/215/problem-2-9/#comments">3 Comments<span class="screen-reader-text"> on Problem 2-9: Differentiating Polynomial and Rational Functions</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-215 -->

<article id="post-208" class="post-208 post type-post status-publish format-standard hentry category-integral tag-change-of-variable tag-exponential entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/integral/208/problem-2-8/" rel="bookmark">Problem 2-8: Integration</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Integrating e^x/(1+e^x)</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/integral/208/problem-2-8/" rel="bookmark"><time class="entry-date published updated" datetime="2010-04-10T20:55:54+00:00">April 10, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/integral/" rel="category tag">Integral</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/change-of-variable/" rel="tag">change of variable</a>, <a href="https://www.solved-problems.com/tag/exponential/" rel="tag">exponential</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/integral/208/problem-2-8/#comments">3 Comments<span class="screen-reader-text"> on Problem 2-8: Integration</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-208 -->

<article id="post-169" class="post-169 post type-post status-publish format-standard hentry category-integral tag-absolute tag-absolute-integral tag-definite-integral entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/integral/169/problem-2-7/" rel="bookmark">Problem 2-7: Evaluatin Definite Integrals</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Evaluating definite integrals x^2, sin(x),  2x^3+x-1 and |x|</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/integral/169/problem-2-7/" rel="bookmark"><time class="entry-date published updated" datetime="2010-04-10T19:38:27+00:00">April 10, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/integral/" rel="category tag">Integral</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/absolute/" rel="tag">absolute</a>, <a href="https://www.solved-problems.com/tag/absolute-integral/" rel="tag">absolute integral</a>, <a href="https://www.solved-problems.com/tag/definite-integral/" rel="tag">definite integral</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/integral/169/problem-2-7/#comments">1 Comment<span class="screen-reader-text"> on Problem 2-7: Evaluatin Definite Integrals</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-169 -->

<article id="post-156" class="post-156 post type-post status-publish format-standard hentry category-precalculus tag-even tag-even-function tag-function tag-odd tag-odd-function entry">
	<header class="entry-header">
		<h2 class="entry-title"><a href="https://www.solved-problems.com/calculus/precalculus/156/problem-2-6/" rel="bookmark">Problem 2-6: Odd and Even Functions</a></h2>	</header><!-- .entry-header -->

	
	<div class="entry-content">
		<p>Determining odd and even functions for sin(x), cos(x), sin(x)cos(x), x*sin(x), x^2 and sin(x)+cos(x)</p>
	</div><!-- .entry-content -->

	<footer class="entry-footer">
		<span class="byline"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M12 12c2.21 0 4-1.79 4-4s-1.79-4-4-4-4 1.79-4 4 1.79 4 4 4zm0 2c-2.67 0-8 1.34-8 4v2h16v-2c0-2.66-5.33-4-8-4z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted by</span><span class="author vcard"><a class="url fn n" href="https://www.solved-problems.com/author/yaz/">Yaz</a></span></span><span class="posted-on"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><defs><path id="a" d="M0 0h24v24H0V0z"></path></defs><clipPath id="b"><use xlink:href="#a" overflow="visible"></use></clipPath><path clip-path="url(#b)" d="M12 2C6.5 2 2 6.5 2 12s4.5 10 10 10 10-4.5 10-10S17.5 2 12 2zm4.2 14.2L11 13V7h1.5v5.2l4.5 2.7-.8 1.3z"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/156/problem-2-6/" rel="bookmark"><time class="entry-date published updated" datetime="2010-04-10T06:26:58+00:00">April 10, 2010</time></a></span><span class="cat-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 4H4c-1.1 0-1.99.9-1.99 2L2 18c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V8c0-1.1-.9-2-2-2h-8l-2-2z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Posted in</span><a href="https://www.solved-problems.com/topic/calculus/precalculus/" rel="category tag">Precalculus</a></span><span class="tags-links"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21.41 11.58l-9-9C12.05 2.22 11.55 2 11 2H4c-1.1 0-2 .9-2 2v7c0 .55.22 1.05.59 1.42l9 9c.36.36.86.58 1.41.58.55 0 1.05-.22 1.41-.59l7-7c.37-.36.59-.86.59-1.41 0-.55-.23-1.06-.59-1.42zM5.5 7C4.67 7 4 6.33 4 5.5S4.67 4 5.5 4 7 4.67 7 5.5 6.33 7 5.5 7z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><span class="screen-reader-text">Tags: </span><a href="https://www.solved-problems.com/tag/even/" rel="tag">even</a>, <a href="https://www.solved-problems.com/tag/even-function/" rel="tag">even function</a>, <a href="https://www.solved-problems.com/tag/function/" rel="tag">function</a>, <a href="https://www.solved-problems.com/tag/odd/" rel="tag">odd</a>, <a href="https://www.solved-problems.com/tag/odd-function/" rel="tag">odd function</a></span><span class="comments-link"><svg class="svg-icon" width="16" height="16" aria-hidden="true" role="img" focusable="false" viewBox="0 0 24 24" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M21.99 4c0-1.1-.89-2-1.99-2H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h14l4 4-.01-18z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg><a href="https://www.solved-problems.com/calculus/precalculus/156/problem-2-6/#comments">1 Comment<span class="screen-reader-text"> on Problem 2-6: Odd and Even Functions</span></a></span>	</footer><!-- .entry-footer -->
</article><!-- #post-156 -->

	<nav class="navigation pagination" aria-label="Posts">
		<h2 class="screen-reader-text">Posts navigation</h2>
		<div class="nav-links"><span aria-current="page" class="page-numbers current">1</span>
<a class="page-numbers" href="https://www.solved-problems.com/topic/calculus/page/2/">2</a>
<a class="next page-numbers" href="https://www.solved-problems.com/topic/calculus/page/2/"><span class="nav-next-text">Older posts</span> <svg class="svg-icon" width="22" height="22" aria-hidden="true" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 6L8.59 7.41 13.17 12l-4.58 4.59L10 18l6-6z"></path><path d="M0 0h24v24H0z" fill="none"></path></svg></a></div>
	</nav>		</main><!-- #main -->
	</div><!-- #primary -->


	</div><!-- #content -->

	<footer id="colophon" class="site-footer">
		
	<aside class="widget-area" aria-label="Footer">
							<div class="widget-column footer-widget-1">
					<section id="search-2" class="widget widget_search"><form role="search" method="get" class="search-form" action="https://www.solved-problems.com/">
				<label>
					<span class="screen-reader-text">Search for:</span>
					<input type="search" class="search-field" placeholder="Search &hellip;" value="" name="s" />
				</label>
				<input type="submit" class="search-submit" value="Search" />
			</form></section>
		<section id="recent-posts-2" class="widget widget_recent_entries">
		<h2 class="widget-title">Recent Posts</h2><nav aria-label="Recent Posts">
		<ul>
											<li>
					<a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/resistive-circuits/1760/solving-a-simple-circuit-of-three-elements/">Solving a Simple Circuit of Three Elements</a>
									</li>
											<li>
					<a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/basic-concepts/1751/power-and-energy-conservation/">Power and Energy Conservation</a>
									</li>
											<li>
					<a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/basic-concepts/1740/circuit-containing-only-sources/">Circuit Containing Only Sources</a>
									</li>
											<li>
					<a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/resistive-circuits/1555/find-the-current-using-superposition/">Find the current using superposition.</a>
									</li>
											<li>
					<a href="https://www.solved-problems.com/youtube/1517/youtube-channel/">YouTube Channel</a>
									</li>
					</ul>

		</nav></section><section id="recent-comments-2" class="widget widget_recent_comments"><h2 class="widget-title">Recent Comments</h2><nav aria-label="Recent Comments"><ul id="recentcomments"><li class="recentcomments"><span class="comment-author-link">gohan</span> on <a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/385/problem-1-12-voltage-sources-determine-node-voltages/#comment-496800">Problem 1-12: Using Voltage Sources to Determine Node Voltages</a></li><li class="recentcomments"><span class="comment-author-link">Anandarupa Neogi</span> on <a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/resistive-circuits/1438/mesh-current-analysis-problem/#comment-496231">Mesh (Current) Analysis Problem</a></li><li class="recentcomments"><span class="comment-author-link">ermi</span> on <a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/641/nodal-analysis-dependent-current-source/#comment-492604">Nodal Analysis &#8211; Dependent Current Source</a></li><li class="recentcomments"><span class="comment-author-link"><a href="https://creativesaplings.com/" class="url" rel="ugc external nofollow">LGR239</a></span> on <a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/resistive-circuits/1226/mesh-analysis-supermesh/#comment-488052">Mesh Analysis &#8211; Supermesh</a></li><li class="recentcomments"><span class="comment-author-link">phonydarkmaster</span> on <a href="https://www.solved-problems.com/circuits/electrical-circuits-problems/resistive-circuits/1226/mesh-analysis-supermesh/#comment-486576">Mesh Analysis &#8211; Supermesh</a></li></ul></nav></section><section id="archives-2" class="widget widget_archive"><h2 class="widget-title">Archives</h2><nav aria-label="Archives">
			<ul>
					<li><a href='https://www.solved-problems.com/date/2019/10/'>October 2019</a></li>
	<li><a href='https://www.solved-problems.com/date/2019/08/'>August 2019</a></li>
	<li><a href='https://www.solved-problems.com/date/2019/07/'>July 2019</a></li>
	<li><a href='https://www.solved-problems.com/date/2015/04/'>April 2015</a></li>
	<li><a href='https://www.solved-problems.com/date/2014/09/'>September 2014</a></li>
	<li><a href='https://www.solved-problems.com/date/2013/10/'>October 2013</a></li>
	<li><a href='https://www.solved-problems.com/date/2013/09/'>September 2013</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/11/'>November 2010</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/10/'>October 2010</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/09/'>September 2010</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/07/'>July 2010</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/06/'>June 2010</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/05/'>May 2010</a></li>
	<li><a href='https://www.solved-problems.com/date/2010/04/'>April 2010</a></li>
			</ul>

			</nav></section><section id="categories-2" class="widget widget_categories"><h2 class="widget-title">Categories</h2><nav aria-label="Categories">
			<ul>
					<li class="cat-item cat-item-145"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/ac-steady-state/">AC Steady State Analysis</a>
</li>
	<li class="cat-item cat-item-100"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/basic-concepts/">Basic Concepts</a>
</li>
	<li class="cat-item cat-item-101"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/capacitors-and-inductors/">Capacitors and Inductors</a>
</li>
	<li class="cat-item cat-item-21"><a href="https://www.solved-problems.com/topic/calculus/derivative/">Derivative</a>
</li>
	<li class="cat-item cat-item-99"><a href="https://www.solved-problems.com/topic/circuits/circuits-articles/">Electrical Circuits Articles</a>
</li>
	<li class="cat-item cat-item-143"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-contests/">Electrical Circuits Contests</a>
</li>
	<li class="cat-item cat-item-105"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/">Electrical Circuits Problems</a>
</li>
	<li class="cat-item cat-item-126"><a href="https://www.solved-problems.com/topic/calculus/integral/">Integral</a>
</li>
	<li class="cat-item cat-item-128"><a href="https://www.solved-problems.com/topic/calculus/limits/">Limits</a>
</li>
	<li class="cat-item cat-item-130"><a href="https://www.solved-problems.com/topic/calculus/precalculus/">Precalculus</a>
</li>
	<li class="cat-item cat-item-106"><a href="https://www.solved-problems.com/topic/circuits/electrical-circuits-problems/resistive-circuits/">Resistive Circuits</a>
</li>
	<li class="cat-item cat-item-151"><a href="https://www.solved-problems.com/topic/control-systems/stability/">Stability</a>
</li>
	<li class="cat-item cat-item-163"><a href="https://www.solved-problems.com/topic/youtube/">YouTube</a>
</li>
			</ul>

			</nav></section><section id="meta-2" class="widget widget_meta"><h2 class="widget-title">Meta</h2><nav aria-label="Meta">
		<ul>
						<li><a href="https://www.solved-problems.com/wp-login.php">Log in</a></li>
			<li><a href="https://www.solved-problems.com/feed/">Entries feed</a></li>
			<li><a href="https://www.solved-problems.com/comments/feed/">Comments feed</a></li>

			<li><a href="https://wordpress.org/">WordPress.org</a></li>
		</ul>

		</nav></section><section id="tag_cloud-2" class="widget widget_tag_cloud"><h2 class="widget-title">Tags</h2><nav aria-label="Tags"><div class="tagcloud"><a href="https://www.solved-problems.com/tag/branch/" class="tag-cloud-link tag-link-14 tag-link-position-1" style="font-size: 8pt;" aria-label="branch (2 items)">branch</a>
<a href="https://www.solved-problems.com/tag/capacitor/" class="tag-cloud-link tag-link-107 tag-link-position-2" style="font-size: 8pt;" aria-label="capacitor (2 items)">capacitor</a>
<a href="https://www.solved-problems.com/tag/circuit-reduction/" class="tag-cloud-link tag-link-41 tag-link-position-3" style="font-size: 10.666666666667pt;" aria-label="circuit reduction (3 items)">circuit reduction</a>
<a href="https://www.solved-problems.com/tag/conductance/" class="tag-cloud-link tag-link-49 tag-link-position-4" style="font-size: 8pt;" aria-label="conductance (2 items)">conductance</a>
<a href="https://www.solved-problems.com/tag/current-divider/" class="tag-cloud-link tag-link-48 tag-link-position-5" style="font-size: 8pt;" aria-label="current divider (2 items)">current divider</a>
<a href="https://www.solved-problems.com/tag/current-source/" class="tag-cloud-link tag-link-10 tag-link-position-6" style="font-size: 22pt;" aria-label="Current Source (12 items)">Current Source</a>
<a href="https://www.solved-problems.com/tag/current-source-power/" class="tag-cloud-link tag-link-47 tag-link-position-7" style="font-size: 8pt;" aria-label="current source power (2 items)">current source power</a>
<a href="https://www.solved-problems.com/tag/dependent-current-source/" class="tag-cloud-link tag-link-72 tag-link-position-8" style="font-size: 8pt;" aria-label="dependent current source (2 items)">dependent current source</a>
<a href="https://www.solved-problems.com/tag/dependent-voltage-source/" class="tag-cloud-link tag-link-84 tag-link-position-9" style="font-size: 12.888888888889pt;" aria-label="Dependent Voltage Source (4 items)">Dependent Voltage Source</a>
<a href="https://www.solved-problems.com/tag/differentiation-formula/" class="tag-cloud-link tag-link-31 tag-link-position-10" style="font-size: 8pt;" aria-label="Differentiation Formula (2 items)">Differentiation Formula</a>
<a href="https://www.solved-problems.com/tag/ebook/" class="tag-cloud-link tag-link-76 tag-link-position-11" style="font-size: 8pt;" aria-label="ebook (2 items)">ebook</a>
<a href="https://www.solved-problems.com/tag/element/" class="tag-cloud-link tag-link-8 tag-link-position-12" style="font-size: 10.666666666667pt;" aria-label="Element (3 items)">Element</a>
<a href="https://www.solved-problems.com/tag/energy/" class="tag-cloud-link tag-link-5 tag-link-position-13" style="font-size: 12.888888888889pt;" aria-label="Energy (4 items)">Energy</a>
<a href="https://www.solved-problems.com/tag/function/" class="tag-cloud-link tag-link-18 tag-link-position-14" style="font-size: 8pt;" aria-label="function (2 items)">function</a>
<a href="https://www.solved-problems.com/tag/independent-sources/" class="tag-cloud-link tag-link-85 tag-link-position-15" style="font-size: 20.444444444444pt;" aria-label="Independent Sources (10 items)">Independent Sources</a>
<a href="https://www.solved-problems.com/tag/indeterminate-form/" class="tag-cloud-link tag-link-55 tag-link-position-16" style="font-size: 8pt;" aria-label="indeterminate form (2 items)">indeterminate form</a>
<a href="https://www.solved-problems.com/tag/kcl/" class="tag-cloud-link tag-link-56 tag-link-position-17" style="font-size: 17.333333333333pt;" aria-label="KCL (7 items)">KCL</a>
<a href="https://www.solved-problems.com/tag/kvl/" class="tag-cloud-link tag-link-57 tag-link-position-18" style="font-size: 14.666666666667pt;" aria-label="KVL (5 items)">KVL</a>
<a href="https://www.solved-problems.com/tag/kvl_kcl/" class="tag-cloud-link tag-link-164 tag-link-position-19" style="font-size: 12.888888888889pt;" aria-label="KVL_KCL (4 items)">KVL_KCL</a>
<a href="https://www.solved-problems.com/tag/linear/" class="tag-cloud-link tag-link-17 tag-link-position-20" style="font-size: 8pt;" aria-label="linear (2 items)">linear</a>
<a href="https://www.solved-problems.com/tag/nodal-analysis/" class="tag-cloud-link tag-link-83 tag-link-position-21" style="font-size: 22pt;" aria-label="Nodal Analysis (12 items)">Nodal Analysis</a>
<a href="https://www.solved-problems.com/tag/nodal_analysis/" class="tag-cloud-link tag-link-171 tag-link-position-22" style="font-size: 18.444444444444pt;" aria-label="Nodal_Analysis (8 items)">Nodal_Analysis</a>
<a href="https://www.solved-problems.com/tag/node/" class="tag-cloud-link tag-link-12 tag-link-position-23" style="font-size: 8pt;" aria-label="node (2 items)">node</a>
<a href="https://www.solved-problems.com/tag/node-voltage/" class="tag-cloud-link tag-link-58 tag-link-position-24" style="font-size: 8pt;" aria-label="node voltage (2 items)">node voltage</a>
<a href="https://www.solved-problems.com/tag/ohms-law/" class="tag-cloud-link tag-link-132 tag-link-position-25" style="font-size: 10.666666666667pt;" aria-label="Ohm&#039;s law (3 items)">Ohm&#039;s law</a>
<a href="https://www.solved-problems.com/tag/power/" class="tag-cloud-link tag-link-6 tag-link-position-26" style="font-size: 19.555555555556pt;" aria-label="Power (9 items)">Power</a>
<a href="https://www.solved-problems.com/tag/power-calculation/" class="tag-cloud-link tag-link-43 tag-link-position-27" style="font-size: 12.888888888889pt;" aria-label="power calculation (4 items)">power calculation</a>
<a href="https://www.solved-problems.com/tag/power_energy/" class="tag-cloud-link tag-link-177 tag-link-position-28" style="font-size: 10.666666666667pt;" aria-label="Power_Energy (3 items)">Power_Energy</a>
<a href="https://www.solved-problems.com/tag/rational-function/" class="tag-cloud-link tag-link-50 tag-link-position-29" style="font-size: 8pt;" aria-label="rational function (2 items)">rational function</a>
<a href="https://www.solved-problems.com/tag/reference-node/" class="tag-cloud-link tag-link-44 tag-link-position-30" style="font-size: 10.666666666667pt;" aria-label="reference node (3 items)">reference node</a>
<a href="https://www.solved-problems.com/tag/resistor/" class="tag-cloud-link tag-link-11 tag-link-position-31" style="font-size: 8pt;" aria-label="Resistor (2 items)">Resistor</a>
<a href="https://www.solved-problems.com/tag/solving-equations/" class="tag-cloud-link tag-link-78 tag-link-position-32" style="font-size: 12.888888888889pt;" aria-label="solving equations (4 items)">solving equations</a>
<a href="https://www.solved-problems.com/tag/source/" class="tag-cloud-link tag-link-7 tag-link-position-33" style="font-size: 18.444444444444pt;" aria-label="Source (8 items)">Source</a>
<a href="https://www.solved-problems.com/tag/source_division/" class="tag-cloud-link tag-link-166 tag-link-position-34" style="font-size: 12.888888888889pt;" aria-label="source_division (4 items)">source_division</a>
<a href="https://www.solved-problems.com/tag/supernode/" class="tag-cloud-link tag-link-70 tag-link-position-35" style="font-size: 10.666666666667pt;" aria-label="supernode (3 items)">supernode</a>
<a href="https://www.solved-problems.com/tag/superposition/" class="tag-cloud-link tag-link-95 tag-link-position-36" style="font-size: 16.222222222222pt;" aria-label="Superposition (6 items)">Superposition</a>
<a href="https://www.solved-problems.com/tag/superposition-method/" class="tag-cloud-link tag-link-114 tag-link-position-37" style="font-size: 12.888888888889pt;" aria-label="Superposition Method (4 items)">Superposition Method</a>
<a href="https://www.solved-problems.com/tag/superposition_method/" class="tag-cloud-link tag-link-167 tag-link-position-38" style="font-size: 12.888888888889pt;" aria-label="Superposition_Method (4 items)">Superposition_Method</a>
<a href="https://www.solved-problems.com/tag/thevenin-equivalent-circuit/" class="tag-cloud-link tag-link-117 tag-link-position-39" style="font-size: 12.888888888889pt;" aria-label="thevenin equivalent circuit (4 items)">thevenin equivalent circuit</a>
<a href="https://www.solved-problems.com/tag/thevenin_norton/" class="tag-cloud-link tag-link-165 tag-link-position-40" style="font-size: 10.666666666667pt;" aria-label="Thevenin_Norton (3 items)">Thevenin_Norton</a>
<a href="https://www.solved-problems.com/tag/thevenin/" class="tag-cloud-link tag-link-116 tag-link-position-41" style="font-size: 12.888888888889pt;" aria-label="Thévenin (4 items)">Thévenin</a>
<a href="https://www.solved-problems.com/tag/turning-sources-off/" class="tag-cloud-link tag-link-120 tag-link-position-42" style="font-size: 12.888888888889pt;" aria-label="Turning sources off (4 items)">Turning sources off</a>
<a href="https://www.solved-problems.com/tag/voltage-divider/" class="tag-cloud-link tag-link-67 tag-link-position-43" style="font-size: 10.666666666667pt;" aria-label="voltage divider (3 items)">voltage divider</a>
<a href="https://www.solved-problems.com/tag/voltage-division-rule/" class="tag-cloud-link tag-link-68 tag-link-position-44" style="font-size: 8pt;" aria-label="voltage division rule (2 items)">voltage division rule</a>
<a href="https://www.solved-problems.com/tag/voltage-source/" class="tag-cloud-link tag-link-9 tag-link-position-45" style="font-size: 21.333333333333pt;" aria-label="Voltage Source (11 items)">Voltage Source</a></div>
</nav></section>					</div>
					</aside><!-- .widget-area -->

			<div class="site-info">
										<a class="site-name" href="https://www.solved-problems.com/" rel="home">Solved Problems</a>,
						<a href="https://wordpress.org/" class="imprint">
				Proudly powered by WordPress.			</a>
								</div><!-- .site-info -->
	</footer><!-- #colophon -->

</div><!-- #page -->

<script src='https://www.solved-problems.com/wp-content/themes/twentynineteen/js/priority-menu.js?ver=20200129' id='twentynineteen-priority-menu-js'></script>
<script src='https://www.solved-problems.com/wp-content/themes/twentynineteen/js/touch-keyboard-navigation.js?ver=20221101' id='twentynineteen-touch-navigation-js'></script>
<script defer src='https://stats.wp.com/e-202413.js' id='jetpack-stats-js'></script>
<script id='jetpack-stats-js-after'>
_stq = window._stq || [];
_stq.push([ "view", {v:'ext',blog:'13171459',post:'0',tz:'0',srv:'www.solved-problems.com',j:'1:12.3'} ]);
_stq.push([ "clickTrackerInit", "13171459", "0" ]);
</script>
	<script>
	/(trident|msie)/i.test(navigator.userAgent)&&document.getElementById&&window.addEventListener&&window.addEventListener("hashchange",function(){var t,e=location.hash.substring(1);/^[A-z0-9_-]+$/.test(e)&&(t=document.getElementById(e))&&(/^(?:a|select|input|button|textarea)$/i.test(t.tagName)||(t.tabIndex=-1),t.focus())},!1);
	</script>
	
</body>
</html>
