College Submissions

Limit of a sequence (Calculus 1)

2015-01-28T18:46:00.002-08:00

Why is the following statement True ?

limn→+∞ an = L then limn→+∞ 1/n Σk=1n ak = L

If you're using epsilon-delta definitions, here's a proof:

For e>0 there's an N such that for k>N, |ak - L|<e/2.

Take M = |(a1-L) + (a2-L) + .... + (aN-L)|, then for k>N

|a1+...+ak - k*L| <= M + (k-N)e/2

dividing by k

|(a1+....+ak)/k - L| <= M/k + ((k-N)/k)(e/2)

and in the limit k->inf that's e/2, so there's some N' where k>N' implies that's <e.

That means for the given e>0, that N' satifies the limit definition for

lim (a1+...+ak)/k = L

Integer of (1+x²)/abs(1-x²)

2015-01-28T18:45:00.002-08:00

If 1 - x² => 0 :

int ( 1 + x² ) / | 1 - x² | dx

= int ( 1 + x² ) / ( 1 - x² ) dx

= int ( x² - 1 + 2 ) / ( 1 - x² ) dx

= int -1 + 2 / ( 1 - x² ) dx

= int -1 + 2 / [(1 - x)(1 + x)] dx

2 / [(1 - x)(1 + x)] = a / (1 - x) + b / (1 + x)

=> 2 = a(1 + x) + b(1 - x) = a + ax + b - bx = (a - b)x + a + b

=> a = b and a + b = 2

=> a = 1 and b = 1

So :

int ( 1 + x² ) / | 1 - x² | dx

= int -1 + 1 / (1 - x) + 1 / (1 + x) dx

= int -1 - (-1) / (1 - x) + 1 / (1 + x) dx

= [-x - ln(|1 - x|) + ln(|1 + x|)]

Can you do 1 - x² < 0 ?

There are 10 spots in a parking lot arranged in a single row. Three cars are parked randomly but in such a way that no two cars are adjacent to each other. What is the probability that there are at least two empty spots between any two cars?

2015-01-28T18:44:00.001-08:00

You can view this as counting integer solutions. x1,x2,x3,x4 representing the spacing. x1 is the spots before the first car, x2 between the first and the second, x3 between the second and third, x4 after the third.

For the no two cars adjacent the constraints are: x1,x4>=0, x2,x3>=1, x1+x2+x3+x4=7. For at least two spaces, x1,x4>=0, x2,x3>=2, x1+x2+x3+x4=7.

Then you can use stars-and-bars to count the solutions.

http://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29

Subtracting 1 from x2,x3 turns x1,x4>=0, x2,x3>=1, x1+x2+x3+x4=7 into x1,x2,x3,x4>=0, x1+x2+x3+x4=5, and there are C(5+3,3) ways.

Subtracting 2 from x2,x3 turns x1,x4>=0, x2,x3>=2, x1+x2+x3+x4=7 into x1,x2,x3,x4>=0,x1+x2+x3+x4=3, and there are C(3+3,3) ways.

C(3+3,3)/C(5+3,3) = 5/14

For the subject Becquerel(Bq) to disintegerate from 11.5Mbq to 4.6 MBq takes 8 hours. How much percent does it disintegerate per hours?And how big is it after a 24 hours if it starts from 11.5 MBq?

2015-01-28T18:43:00.001-08:00

Final = Initial*e^rt

4.6 = 11.5e^8r

4.6/11.5 = 2/5 = e^8r

ln(2/5) = ln(2) - ln(5) = 8r

(ln(2) - ln(5))/8 = r ~ -11%/hour.

To find how much is left after 24 hours:

Final = 11.5e^{[24(ln(2)-ln(5))/8]} = 11.5e^{[3(ln(2)-ln(5))]} = 11.5(2/5)³

In the following pseudocode, the statement print questionCounter will be executed ____ times.

2014-04-06T21:37:00.003-07:00

num PARTS = 5 num QUESTIONS = 3 partCounter = 1 while partCounter <= PARTS questionCounter = 1 while questionCounter <= QUESTIONS print questionCounter questionCounter = questionCounter + 1 endwhile partCounter = partCounter + 1 endwhile Answer: 15

What is the value of names[4] in the following array? String[] names = {"Jeff", "Dan", "Sally", "Jill", "Allie"};

2014-04-06T21:37:00.001-07:00

Allie

What is the value of times[2][1] in the array that follows? double[][] times = { {23.0, 3.5}, {22.4, 3.6}, {21.3, 3.7} };

2014-04-06T21:36:00.004-07:00

3.7

How many lines are printed on the console when the following for loop is executed?

2014-04-06T21:36:00.002-07:00

for (int i = 2; i < 10; i++) { System.out.println(i); } Answer: 8

How many lines are printed on the console when the following for loop is executed?

2014-04-06T21:35:00.005-07:00

for (int j = 10; j < 40; j *= 2) { System.out.println(j); } Answer: 2

Assume that the variable named entry has a starting value of 9 and number has a value of 3. What is the value of entry after the following statements are executed?

2014-04-06T21:35:00.002-07:00

Question 50 if ((entry > 9) || (entry/number == 3)) entry--; else if (entry == 9) entry++; else entry = 3; Answer: 8

Programming study questions

2014-04-06T21:34:00.003-07:00

Final study guide Multiple Choice Identify the choice that best completes the statement or answers the question. __b__ 1. ____ errors are detected by a compiler. a. Logic c. Input b. Syntax d. Process __d__ 2. After a programmer plans the logic of a program, the next step is ____. a. understanding the problem c. translating the program b. testing the program d. coding the program __a__ 3. The process of walking through a program’s logic on paper before you actually write the program is called ____. a. desk-checking c. pseudocoding b. flowcharting d. testing __d__ 4. Typically, a programmer develops a program’s logic, writes the code, and then ____ the program, which may generate a list of syntax errors. a. runs c. executes b. compiles d. tests __c__ 5. A(n) ____ is a message that is displayed on a monitor, asking the user for a response. a. command prompt c. prompt b. input screen d. input data __d__ 6. A database holds a group of files, often called ____, that together serve the information needs of an organization. a. records c. fields b. characters d. tables __a__ 7. The ____ is the standard terminal symbol for a flowchart. a. circle c. diamond b. lozenge d. square __c__ 8. If a flowchart has six processing steps and a page provides room for only three, you can use a ____ to create the completed flowchart. a. decision symbol c. connector b. lozenge d. terminator _d___ 9. The problem with the following statement is that ____. 100 = grade a. 100 is not a reasonable grade b. 100 should be in quotes c. the data types don’t match d. the value on the left must be a variable name __a__ 10. The major difference between the two main programming styles in use today is the ____. a. use of flowcharts versus pseudocode b. testing procedure used by the programmer c. focus the programmer takes during the earliest planning stages of a project d. programming language used __b__ 11. The following pseudocode is an example of a(n) ____ structure: if firstNumber is bigger than secondNumber then print firstNumber else print secondNumber a. sequence c. loop b. decision d. nested __d__ 12. Fill in the blank in the following pseudocode: if someCondition is true then do oneProcess ____ do theOtherProcess a. then c. do b. while d. else _c___ 13. The following pseudocode is an example of a(n) ____ structure: get number while number is positive add to sum get number a. sequence c. loop b. decision d. nested __c__ 14. Another name for a loop structure is ____. a. execution c. iteration b. selection d. case _b___ 15. The following pseudocode is an example of ____. do stepA do stepB if conditionC is true then do stepD else do stepE endif while conditionF is true do stepG endwhile a. nesting c. single alternative structures b. stacking d. a posttest _a___ 16. The following pseudocode is an example of ____. if conditionA is true then do stepE else do stepB do stepC do stepD endif a. nesting c. a posttest b. stacking d. a pretest __d__ 17. Years ago, programmers could avoid using structure by inserting a “____” statement into their pseudocode. a. loop c. next b. go next d. go to __b__ 18. Structured programs can be easily broken down into routines or ____ that can be assigned to any number of programmers. a. segments c. units b. modules d. sequences __b__ 19. ____ is considered to be a convenience structure. a. if-then-else c. case b. while d. sequence __c__ 20. In a case structure, the term ____ means “if none of the other cases were true.” a. else c. default b. then d. loop __a__ 21. A case structure can be replaced by one or more ____ structures. a. if-then-else c. do-until b. do-while d. while __d__ 22. In a ____ loop, the loop body continues to execute as long as the answer to the controlling question is yes, or true. a. do-then c. do-until b. do-when d. do-while __c__ 23. ____ is an example of a pretest loop. a. do-while c. while b. do-until d. case __d__ 24. People who use computer programs are called ____. a. managers c. stakeholders b. programmers d. end users __c__ 25. The ____ of documentation is typically written first. a. input c. internal program b. output d. external program __a__ 26. ____ is the process of paying attention to important properties while ignoring nonessential details. a. Abstraction c. Reusability b. Modularization d. Direction _c___ 27. ____ is the feature of programs that assures you a module has been tested and proven to function correctly. a. Modularization c. Reliability b. Abstraction d. Reusability _d___ 28. When a program or module uses another module, you can refer to the main program as the ____ program. a. director c. called b. calling d. parent _a___ 29. The ____ statement is used to indicate the end of a module. a. stop c. return b. end d. done _d___ 30. The name that is best suited to a module that calculates overtime pay is ____. a. calcO() c. calculate overtime() b. cO() d. calculateOvertime() __b__ 31. The structure that is used in a binary selection is ____. a. if-then c. while b. if-then-else d. do-while __c__ 32. Boolean expressions are named after ____. a. Harold Boolean c. George Boole b. Henry Boole d. Gerhardt Boolean __a__ 33. In ____ the equal sign (=) is used to express testing equivalency. a. VisualBasic c. C++ b. Java d. C# __d__ 34. The pseudocode that produces the same result as the following is ____. if customerAge >= 65 then discount = 0.10 else discount = 0 endif a. if customerAge > 65 then discount = 0.10 else discount = 0 endif b. if customerAge < 65 then discount = 0.10 else discount = 0 endif c. if customerAge > 65 then discount = 0 else discount = 0.10 endif d. if customerAge < 65 then discount = 0 else discount = 0.10 endif _c___ 35. The decision structure that is logically equivalent to the following is ___. if customerCode not equal to 1 then discount = 0.25 else discount = 0.50 endif a. if customerCode > 1 then discount = 0.50 else discount = 0.25 endif b. if customerCode < 1 then discount = 0.50 else discount = 0.25 endif c. if customerCode = 1 then discount = 0.50 else discount = 0.25 endif d. if customerCode = 1 then discount = 0.20 else discount = 0.50 endif __d__ 36. When you need to ask multiple questions before an outcome is determined, you must create a(n) ____ condition. a. dual-alternative c. single-alternative b. nested d. compound __b__ 37. A series of nested if statements can also be called a(n) ____ statement. a. n-alternative if c. case b. cascading if d. loop __d__ 38. ____ are diagrams used in mathematics and logic to help describe the truth of an entire expression based on the truth of its parts. a. Decision matrices c. Truth diagrams b. Decision diagrams d. Truth tables __d__ 39. For maximum efficiency, a good rule of thumb in an OR decision is to ____. a. first ask the question that is more likely to be true b. first ask the question that is more likely to be false c. rewrite as an and decision and ask the question more likely to be true d. rewrite as an and decision and ask the question more likely to be false __c__ 40. The symbol that represents a logical OR in Java, C++, and C# is ____. a. % c. || b. $ d. ^ ___a_ 41. Suppose a movie theater manager says, “Provide a discount to patrons who are under 13 years old and those who are over 64 years old; otherwise, charge the full price.” Which statement will implement this logic correctly? a. if patronAge < 13 AND patronAge > 64 then price = discountPrice else price = fullPrice endif b. if patronAge > 13 AND patronAge < 64 then price = discountPrice else price = fullPrice endif c. if patronAge < 13 OR patronAge > 64 then price = discountPrice else price = fullPrice endif d. if patronAge > 13 OR patronAge < 64 then price = discountPrice else price = fullPrice endif __c__ 42. The logical OR operator can be compared to ____ in terms of precedence. a. addition c. multiplication b. subtraction d. division _b___ 43. The type of nested if-then-else structure that could be replaced with a case structure is ____. a. inner nested if within the if portion of the outer if b. inner if within the else portion of the outer if c. one that uses a logical AND d. one that uses a logical OR __b__ 44. When creating a decision table, you must determine how many possible Boolean value combinations exist for the conditions. If there are two conditions, ____ combinations will exist. a. 2 c. 8 b. 4 d. 16 __a__ 45. The first step in a loop is typically ____. a. compare the variable to a value that determines if the loop stops or continues b. initialize the variable c. increment the variable d. perform the loop action __d__ 46. In the following pseudocode fragment, the while loop will terminate when ____. counter = 10 while response = ‘Y’ print counter counter = counter - 1 print “Do you want to see the next counter? Y or N” get response endwhile a. counter = 0 c. response = ‘Y’ b. the while loop will not terminate. d. response = ‘N’ __a__ 47. Once a program enters the body of a structured loop, ____. a. the entire loop must execute b. the loop can be terminated with a break statement c. the loop will execute indefinitely d. a decision statement will be evaluated __d__ 48. The following loop will execute ____ times. counter = 0 while counter <= 10 print “Hello” counter = counter + 1 endwhile a. 0 times c. 10 times b. 9 times d. 11 times _a___ 49. The ____ loop provides three actions in one compact statement. a. for c. do until b. while d. repeat _c___ 50. In a ____ loop, the body of the loop will always execute at least once. a. for c. do until b. while d. repeat _c___ 51. The statement that is true of a structured loop is that ____. a. the loop can exit from any point b. the loop body must execute at least once c. the loop condition represents the only exit from the loop d. the loop can repeat an infinite number of times __c__ 52. A(n) ____ is increased by an arbitrary value, whereas a(n) ____ is usually increased by one. a. summary, total c. accumulator, counter b. counter, accumulator d. counter, summary __b__ 53. ____ is another name for an array. a. group c. matrix b. sequence d. subscript __c__ 54. In all languages, subscript values must be ____. a. characters c. real numbers b. non-sequential d. non-negative __c__ 55. An array can be used to replace ____. a. records c. nested decisions b. methods d. loops __c__ 56. Of the following, ____, is true of arrays. a. An array subscript can be a number or a character. b. Using a numeric constant as a subscript is generally much better than using a variable. c. A named constant equal to the array size can be used to subscript the array. d. In Java, when an array is declared, a constant representing the size is automatically created. __b__ 57. The type of loop____, is used to set the initial value for array variables. a. declaration c. implied b. initialization d. direct __d__ 58. Providing array values is called ____. a. creating the array c. accumulating the array b. declaring the array d. populating the array __c__ 59. Another name for an array is a(n) ____. a. vector c. collection b. table d. set __a__ 60. ____ is true of arrays. a. Only whole numbers can be used as array subscripts. b. Only whole numbers can be stored in arrays. c. Arrays cause more work for the programmer, but allow faster program execution. d. Array elements cannot be reset after the array is declared.

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2013-11-18T16:45:00.000-08:00

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Chemistry Multiple Choice

2013-05-22T15:10:00.000-07:00

1 In which direction will the point of equilibrium shift when a catalyst is added to the following equilibrium system?

KNO3 + 34.7 kJ K+1 (aq) + NO3-1 (aq)

a.Shift to the right
b.Shift to the left
c.No shift

2.The magnitude of Keq depends on
a.Initial concentration of reactants
b.Presence of a catalyst
c.Temperature
d.Volume of reaction vessel

3.In which direction will the point of equilibrium shift when the pressure is decreased in the following equilibrium?

H2 (g) + Cl2 (g) 2 HCl (g)
a.Shift to the right
b.Shift to the left
c.No shift

4.The equilibrium constant can change significantly with a change in
a.Concentration
b.Catalyst
c.Temperature
d.Pressure

5.In the following equilibrium, when sodium ion is removed, the concentration of chloride ion will
Na+1 (aq) + Cl-1 (aq) NaCl (s)

a.Increase
b.Decrease
c.Remain the same
----------------------------------------------------------------------------------

1. In which direction will the point of equilibrium shift when a catalyst is added to the following equilibrium system?

KNO3 + 34.7 kJ ---> K+ (aq) + NO3- (aq)

c.No shift

Catalyst won't affect equilibrium and the rates, as it only speeds up the reaction by decreasing the activiation energy.

2.The magnitude of Keq depends on

c.Temperature

Fact.

3.In which direction will the point of equilibrium shift when the pressure is decreased in the following equilibrium?

H2 (g) + Cl2 (g) ---> 2 HCl (g)

c.No shift

When pressure is decreased, equilibrium shifts to the greatest number of moles; there are equal number of moles on both sides.

4.The equilibrium constant can change significantly with a change in

c.Temperature

Only temperature effects rate constant.

5.In the following equilibrium, when sodium ion is removed, the concentration of chloride ion will
Na+ (aq) + Cl- (aq)---> NaCl (s)

a.Increase

If Na+ is taken out, equilibrium will shift to the left to increase [Cl-].

A 15mg strip of Magnesium metal reacts in 5.0 mL of 1.0M HCl over a given period. Evaluate the (mol HCl)/(mol Mg) ratio for the reaction. moles of each Mg and HCl by using their masses?

2013-05-18T15:08:00.000-07:00

First convert mass to grams: 15 mg = 0.015 g

n(Mg) = 0.015 g / 24.31 g-mol = 0.00062 mol

For HCl, determine from product of volume (in liters) and molarity:

n(HCl) = (0.005 L)(1.0 M) = 0.0050 mol

So the ratio (mol HCl/mol Mg) = 0.0050 / 0.00062 = 250 / 31

If 2 moles of an ideal gas at STP are subjected to a new pressure of 24.7 kPa, what will be the volume of the gas? Answer in units of L.

2013-05-15T15:08:00.000-07:00

PV=nRT... Solve for V
V=nRT/P
V=2 mol x 8.314 LkPa/molK x 273K / 24.7kPa
V=184 L

You are studying flower color in tulips. Yellow is dominant over white. You have discovered a yellow flower but are unsure of its precise genotype. What are the possible genotype(s) for this flower?

2013-05-11T15:07:00.000-07:00

Yy or YY

A mother is a carrier for color blindness and a father is affected by color blindness.Is this trait dominant?

2013-05-09T15:06:00.000-07:00

No. This trait cannot be dominant because the mother is a carrier which means she is a heterozygous. If this trait is dominant, then she will be affected too.

An organism's interrelationships within its environment constitute its?

2013-05-09T15:05:00.000-07:00

A) trophic level
B) dominance rank
C) ecological niche
D) caste
E) habitat

ANSWER
C. Every organisms in an ecosystem plays their respective role (niche) to maintain a balanced environment.

Biology 3 Questions

2013-05-07T15:04:00.000-07:00

1. What determines the size of a grape or a kernel of corn?
a. a combination of genetics and environmental factors
b. genetics alone
c. environmental factors alone

2. Because the grapes or corn come from a single genetic source, you would expect _________________.
a. that all the grapes or corn would fall into a fairly narrow range of values
b. that the grapes or corn would exhibit a great deal of variation
c. that all the grapes or corn would measure exactly the same

3. Which of the following is considered a measure of central tendency (indicates what the central value is, rather than the deviation from the center)?
a. average
b. range
c. variation

ANSWERS
1: A
2: A
3: A

Which of the following are empirical formulas?(Could be as many as 3) 1. H2O2 2. H2SO4 3. S2Cl2 4. CH2O 5. N2 6. C2H4

2013-05-06T15:02:00.000-07:00

Which of the following are empirical formulas?(Could be as many as 3)
1. H2O2
2. H2SO4
3. S2Cl2
4. CH2O
5. N2
6. C2H4

H2O2 = 2(HO) = HO

H2SO4

S2Cl2 = 2(SCl) = SCl

CH2O

N2 = 2N = N

C2H4 = 2(CH2) = CH2

In a sealed container, there is a 1.6 mol sample of ideal gas. the temperature of the room is 22 C and the volume of the container is 1 L. How much pressure is built up in this container?

2013-05-04T15:01:00.001-07:00

Ideal Gas Law is PV = nRt where R = .0821

P * 1L = 1.6mol *.0821 * (273+22)

P = 38.75 atm

What is the [H3O+] (molarity) of a 0.1250 M ethanolamine?

2013-04-04T15:44:00.002-07:00

HOC2H4NH2 + H2O ↔ HOC2H4NH3+ + OH- Kb = 3.20e-5

[OH-] = SQRT(0.1250 * 3.20e-5) = 4.00 x 10^-6 M

Kw = [H+] [OH-]

1.00 x 10^-14 = [H+] (4.00 x 10^-6)

[H+] = 2.50 x 10^-9 M

More info

Determine the number of atoms or molecules in each of the following substances. 1. 0.30 mol F 2. 0.70 mol iron 3. 4.0 mol Na 4. 4.0 mol NH3

2013-04-04T15:42:00.000-07:00

Determine the number of atoms or molecules in each of the following substances.
1. 0.30 mol F
2. 0.70 mol iron
3. 4.0 mol Na
4. 4.0 mol NH3

A mole is simply 6.02x10^23 atoms/molecules/particles/anything, so to figure out how many atoms are in each of those amounts of moles, you need only multiply the number of moles by 6.02x10^23, and then round to the appropriate number of sig figs.

1. .30 * 6.02x10^23 = 1.8x10^23 atoms F.
2. .70 * 6.02x10^23 = 4.2x10^23 atoms Fe.
3. 4.0 * 6.02x10^23 = 2.4x10^24 atoms Na
4. 4.0 * 6.02x10^23 = 2.4x10^24 molecules NH3

It's just like how a dozen is 12. To have a dozen of anything is to have 12 of anything. To have 4 dozen of anything is to have 48 of anything. That's why 4 moles of Na and 4 moles of NH3 come out to be the same number.

Acct 387 Chp 15 16 Solution

2013-02-27T19:55:00.000-08:00

Acct 387 Q1A-IC (Chap. 15 -16) Name_Solution___

Spring Given in Class 1/31

Doran Group#

Total of 16 points.

Part I. Multiple Choice (Circle the Best Answer) 2 points each

1. Presented below is information related to Getty Corporation:

Subscriptions Receivable, Common Stock $ 120,000

Common Stock, $1 par 3,600,000

Common Stock Subscribed 240,000

Paid-in Capital in Excess of Par—Common Stock 210,000

Preferred 8 1/2% Stock, $50 par 1,200,000

Paid-in Capital in Excess of Par—Preferred Stock 240,000

Retained Earnings 900,000

Treasury Common Stock (at cost) 90,000

The total stockholders' equity of Getty Corporation is (Note: Assume Subscriptions receivable is treated as contr-equity)

a. $6,180,000. b. $6,270,000. c. $6,300,000. d. $6,390,000.

2. When a corporation issues shares of its own stock in payment for services, the least appropriate basis for recording this transaction would be

a. the fair market value of the services received

b. the par or stated value of the shares issued.

c. the fair market value of the shares issued

d. All of the above are equally appropriate basis for recording the transaction

3. Nelsen Co. was organized on January 2, 2001, with 100,000 authorized shares of $10 par value common stock. During 2001 Nelsen had the following capital transactions:

January 5—issued 75,000 shares at $14 per share.

July 27—purchased 5,000 shares at $11 per share.

November 25—sold 4,000 shares of treasury stock at $13 per share.

Nelsen used the cost method to record the purchase of the treasury shares. What would be the balance in the Paid-in Capital from Treasury Stock account at December 31, 2001?

a. $0. b. $4,000. c. $8,000. d. $12,000.

4. An entry is not made on the

a. date of declaration.

b. date of record.

c. date of payment.

d. An entry is made on all of these dates.

-Continued on Back Side-

5. A retained earnings appropriation always means the company is

a. setting aside cash for a specific purpose.

b. disclosing managerial policy.

c. preventing unusual losses.

d. improving the debt-equity ratio.

6. Stine Co. had outstanding 2,000 shares of $100 par value 8% cumulative preferred stock and 30,000 shares of $5 par value common stock on December 31, 1998. At December 31, 1998, dividends in arrears on the preferred stock were $20,000. Cash dividends declared in 1999 totaled $60,000. The amounts paid to each class of stock were

Preferred Stock Common Stock

a. $16,000 $44,000

b. $20,000 $40,000

c. $36,000 $24,000

d. $40,000 $20,000

Part II. Fill in the blank (1/2 point each)

Indicate the effect of each of the following transactions on total stockholders' equity by placing an "X" in the appropriate column.

Increase Decrease No Effect

1. The sale of treasury stock for

less than its cost. ___X___ ________ ________

2. Not declaring this year's dividend

On cumulative preferred stock ________ ________ ___X___

3. Declaration of a stock dividend. ________ ________ ___X___

4. Payment of a stock dividend. ________ ________ ___X___

5. Acquiring land by issuing

common stock ___X___ ________ ________

6. Declaration of cash dividend. ________ ___X___ _______

7. Payment of cash dividend. ________ ________ ___X___

8. Conversion of bonds payable

into preferred stock ___X___ ________ ________

Computer Networks MIDTERM EXAM WITH SOLUTIONS

2013-02-25T19:48:00.000-08:00

Midterm Exam - CMPSCI 591 and 453: Computer Networks

a) Suppose all of the network sources send data at a constant bit rate. Would packet-switching or circuit-switching be more desirable in this case? Why? (Answer: circuit-switching is more desirable here as there are no statistical multiplexing gains to be had, and by using circuits, each connection will get a constant amount of bandwidth that matched its CBR rate. On the other hand, circuit-switching has more overhead in terms of signaling, so there is an argument that packet-switching is better here since there is no call setup overhead. I’ll take either answer). Now suppose that all of the network sources are bursty – that they only occasionally have data to send. Would packet-switching or circuit switching be more desirable in this case? Why? (Answer: Packet-switching is better here because there are statistical multiplexing gains – when a source does not have data to send, it will not be allocated bandwidth (that would be idle). Hence this bandwidth is available for use by other sources).

b) Describe the use of the “If-Modified-Since” header in the HTTP protocol. (Answer: When a web client or web cache has a copy of previously requested document, its GET request to the server includes an If-modified-Since line that gives the time at which the browser/cache received the copy of the document. If the document has not been modified at the web server since this time, the web server need not (and will not) send a duplicate copy of the document).

c) What does it mean when we say that control messages are “in-band”? (Answer: It means that control message and data messages may be interleaved with each other on the same connection. Indeed a single message may contain both control information and data). What does it mean when we say that control messages are “out-of-band”? (Answer: It means that control and data messages are carried on separate connections) Give an example of a protocol that has in-band control messages (Answer: examples: HTTP, DNS, TCP, SMTP) and one example of a protocol that has out-of-band control messages (Answer: FTP)

d) Consider a TCP connection between hosts A and B. Suppose that the TCP segments from A to B have source port number x and destination port number y. What are the source and destination port numbers for the segments traveling from B to A? (Answer: source port is y, destination port is x).

e) What is the purpose of the connection-oriented welcoming socket, which the server uses to perform an accept()? Once the accept() is done, does the server use the welcoming socket to communicate back to the client? Explain. (Answer: a connection oriented server waits on the welcoming socket for an incoming connection request. When that connection request arrives a new socket is created at the server for communication back to that client).

f) Suppose a web server has 1000 ongoing TCP connections. How many server-side sockets are used? How many server-side port numbers are used? Briefly (two sentences at most each) explain your answer. (Answer: If there are 1000 ongoing connections, and nothing else happening on the server, there will 1001 sockets in use – the single welcoming socket and the 1000 sockets in use for server-to-client communication. The ONLY server-sideport number in use at the server will be the single port number associated with the welcoming socket, e.g., port 80 on a web server).

Question 2: A reliable data transfer protocol (26 points, 25 minutes)

Consider a scenario in which a Host A wants to simultaneously send messages to Hosts B and C. A is connected to B and C via a broadcast channel – a packet sent by A (e.g., in a single udt_send() operation) is carried by the channel to both B and C. Suppose the broadcast channel connecting A, B, and C

· can independently lose and corrupt messages from A to B and C (and so, for example, a message sent by A might be correctly received at B but not at C)

· has a maximum bounded delay of D (i.e., if a message is sent by A, it will either be lost or arrive at B and/or C within D time units).

· any control messages (e.g., an ACK or NAK) sent by B or C to A will only be received by A but can be lost or corrupted

Design a stop-and-wait-like error-control protocol for reliably transferring a packet from A to B and C, such that A will not get new data from the upper layer until it knows that both B and C have correctly received the current packet. Give a FSM description for A and C (assuming the FSM for B is similar, if it is not similar give the FSM for B as well). Also, give a description of the packet format used.

Solution:

This problem is a variation on the simple stop and wait protocol (rdt3.0). Because the channel may lose messages and because the sender may resend a message that one of the receivers has already received (either because of a premature timeout or because the other

receiver has yet to receive the data correctly), sequence numbers are needed. As in rdt3.0, a 0-bit sequence number will suffice here. Note that the receivers need to identify themselves in their ACK so that the sender will know which receiver sent the ACK, so that it can make sure that it has received ACKs from both receivers.

The sender and receiver FSM are shown in the figure below (note: I do not expect you to have come up with a solution at the level of syntactic detail shown below!). In this problem, the sender state indicates whether the sender has received an ACK from B (only), from C (only) or from neither C nor B. The receiver state indicates which sequence number the receiver is waiting for.

The packet formats are:

Problem 3: Error control potpourri (24 points, 20 minutes)

a) What is the purpose/use of the UDP checksum? (Answer: to detect bit error, i.e., flipped bits, in the UDP segment).

b) Consider the Go-Back-N protocol. Suppose that the size of the sequence number space (number of unique sequence numbers) is N, and the window size is N. Show (give a timeline trace showing the sender, receiver and the messages they exchange over time) that the Go-Back-N protocol will not work correctly in this case. (Answer: suppose that the sequence number space is 0,1 and N=2, i.e., that two messages can be transmitted but not-yet-acknowledged. The timeline below shows an error that can occur)

c) Consider the Go-Back-N protocol, and suppose that base of the senders window is X. Is it possible for the sender to receive an ACK for a packet that has a smaller sequence number than X. If so, sketch out a timeline-diagram showing sender and receiver messages sent and received that shows how this is possible. .If not, explain why this can never happen.

Question 4: Caching and delays (26 points, 20 minutes)

Consider the networks shown in the figure below. There are two user machines m1.a.com and m2.a.com in the network a.com. Suppose the user at m1.a.com types in the URL www.b.com/bigfile.htm into a browser to retrieve a 1Gbit (1000 Mbit) file from www.b.com.

4.1. List the sequence of DNS and HTTP messages sent/received from/by m1.a.com as well as any other messages that leave/enter the a.com network that are not directly sent/received by m1.a.com from the point that the URL is entered into the browser until the file is completely received. Indicate the source and destination of each message. You can assume that every HTTP request by m1.a.com is first directed to the HTTP cache in a.com and that the cache is initially empty, and that all DNS requests are iterated queries.

· M1.a.com needs to resolve the name www.b.com to an IP address so it sends a DNS REQUESTmessage to its local DNS resolver (this takes no time given the assumptions below)

· Local DNS server does not have any information so it contacts a root DNS server with a REQUEST message (this take 500 ms given the assumptions below)

· Root DNS server returns name of DNS Top Level Domain server for .com (this takes 500 ms given the assumptions below)

· Local DNS server contacts .com TLD (this take 500 ms given the assumptions below)

· TLD .com server returns authoritative name server for b.com (this takes 500 ms given the assumptions below)

· Local DNS server contacts authoritative name server for b.com (this takes 100 ms given the assumptions below)

· Authoritative name server for b.com returns IP address of www.b1.com. (this takes 100 ms given the assumptions below)

· HTTP client sends HTTP GET message to www.b1.com, which it sends to the HTTP cache in the a.com network (this takes no time given the assumptions).

· The HTTP cache does not find the requested document in its cache, so it sends the GET request to www.b.com. (this takes 100 ms given the assumptions below)

· www.b.com receives the GE request. There is a 1 sec transmission delay to send the 1Gbps file from www.b.com to R2. If we assume that as soon as the first few bits of the file arrive at R1, that they are forwarded on the 1Mbps R2-to-R1 link, then this delay can be ignored.

· The 1 Gbit file (in smaller packets or in a big chunk, that’s not important here) is transmitted over the 1 Mbps link between R2 and R1. This takes 1000 seconds. There is an additional 100 ms propagation delay.

· There is a 1 sec delay to send the 1Gbps file from R1 to the HTTP cache. If we assume that as soon as the first few bits of the file arrive at the cache, that they are forwarded to the cache, then this delay can be ignored.

· There is a 1 sec delay to send the 1Gbps file from the HTTP cache to m1.a.com. If we assume that as soon as the first few bits of the file arrive at the cache, that they are forwarded to the cache, then this delay can be ignored.

· The total delay is thus: .5 + .5 + .5 +.5 +.1 + .1 + 1 + 1000 +1+1 = 1105.2 secs (1002.2 is also an OK answer).

4.2. How much time does it take to accomplish the steps you outlined in your answer to 4.1? Explain how you arrived at this answer. In answering this question, you can make the following assumptions

· The packets containing any DNS commands and HTTP commands such as GET are very small compared to the size of the file, and thus their transmission times (but not their propagation times) can be neglected.

· Propagation delays within the LAN are small enough to be ignored. The propagation from router R1 to router R2 is 100 ms.

· The propagation delay from anywhere in a.com to any other site in the Internet (except b.com) is 500 ms.

(See above for answer. Note that we have neglected to account for TCP hand-shaking delays for the HTTP exchanges!)

4.3. Now assume that machine m2.a.com makes a request to exactly the same URL that m1.a.com made. List the sequence of DNS and HTTP messages sent/received from/by m2.a.com as well as any other messages that leave/enter the a.com network that are not directly sent/received by m2.a.com from the point that the URL is entered into the browser until the file is completely received. Indicate the source and destination of each message. [Hint: make sure you consider caching here]

· m2.a.com needs to resolve the name www.b.com to an IP address so it sends a DNS REQUEST message to its local DNS resolver (this takes no time given the assumptions above)

· The local DNS server looks in its cache and finds the IP address for www.b.com, since m1.a.com had just requested that that name be resolved, and returns the IP address to m2.b.com. (this takes no time given the assumptions above)

· HTTP client at m2.a.com sends HTTP GET message to www.b1.com, which it sends to the HTTP cache in the a.com network (this takes no time given the assumptions).

· The HTTP cache finds the requested document in its cache, so it sends a GET request with an If-Modified-Since to to www.b.com. (this takes 100 ms given the assumptions)

· www.b.com receives the GET request. The document has not changed, so www.b.com sends a short HTTP REPLY message to the HTTP cache in a.com indicating that the cached copy is valid. (this takes 100 ms given the assumptions)

· There is a 1 sec delay to send the 1Gbps file from the HTTP cache to m2.a.com.

· The total delay is thus: .1 + .1 + 1 = 1.2 secs

4.4. How much time does it take to accomplish the steps that you outlined in your answer to 4.3? (Answer: see above)

4.5. Now suppose there is no HTTP cache in network a.com. What is the maximum rate at which machines in a.com can make requests for the file www.b.com/bigfile.htm while keeping the time from when a request is made to when it is satisfied non-infinite in the long run? (Answer: since it takes 1000 secs to send the file from R2tro R1, the maximum rate at which requests to send the file from b.com to a.com is 1 request every 1000 seconds, or an arrival rate of .001 requests/sec.)