exam 2 - uf teaching center · mac 2312 spring 2017 exam 2 a. signyourscantron onthe backat the...

MAC 2312Spring 2017

EXAM 2

A. Sign your scant ron on the back at the bottom in ink.

B. In pencil, write and encode in the spaces indicated:

1) Name (last name, first initial, middle initial)

2) UF ID Number3) Section Number

C. Under "special codes" , code in the test ID number 2, 1.

1 • 3 4 5• 2 345

6 7 8 9 067890

D. At the top right of your answer sheet, for "Test Form Code", encode A.

• BCD E

E. 1) This test consists of seventeen multiple choice questions: four worth 2 points each,ten worth 4 points each and three bonus questions worth 1 point each plus three freeresponse questions worth 22 points for a total ·of73 points. The test is counted outof 70 points. '

2) The time allowed is 90 minutes.3) You may write on the test.4) Raise your hand if you need more scratch paper, if you have a problem with your test

or any emergency. DO NOT LEAVE YOUR SEAT UNLESS YOU ARE FINISHEDWITH THE TEST.

F. KEEP YOUR SCANTRON COVERED AT ALL TIMES.

G. When you are finished:

1) Before turning in your test, check for transcribing errors. Any mistakes you leave inare there to stay.

2) Bring your test, scratch paper, and scantron to your proctor to turn them in. Beprepared to show your UF ID card.

3) Answers will be posted in E-Learning after the exam.

H. On my honor, I have neither given nor received unauthorized aid doing this

exam.

Signature: __

1A

Be sure to bubble your answers to questions 1-17 on your scantron.

DCT (Direct Comparison Test) AST (Alternating Series Test)

LCT (Limit Comparison Test) TFD (Test for Divergence)

#1 - #4 are worth 2 points each

00 N

Suppose the series converges to L, Lan = L where 0 <L < 00, and SN = 2:.:: an its partialn=l

sum. Answer the next 4 questions:n=l

1. lim an= O.n-too

A. True

B. False

C. Not enough information

2. lim SN = O.N-too

A. True

B. False

C. Not enough information

00

3. The seriesL SN converges.N=l

A. True B. False

MAC 2312 - Spring 2017 - EXAM2

2A

00

4. The seriesL(an + 1) converges.n=l

A. True B. False

#5 - #14 are worth 4 points each

5. Which of the series below can be shown to be divergent using TFD?

A. 'f arct:n(n) fInn00 ,

B. - c·L~n nn

n=l n=l n=l

00 00

D. 2::\12-1 E. Le~n=l n=l

6. Determine whether each of the followingseries converges absolutely (A), conditionally(C) or diverges (D).

00 (-~1)nP. L 7 1

n=5 n +~ cos(mr)

Q. c: Vnn=7 n00 7

R. 2:: 1+1.n=8 n n

A. P(D), Q(D), R(D)

D. P(A), Q(C), R(D)

B. P(A), Q(C), R(C)

E. P(D), Q(C), R(D)

C. P(A), Q(D), R(C)

MAC 2312 - Spring 2017 - EXAM 2

3A

"

00 (_3)n+17. Find the sum of the series L 23n . (Note: starting index: ti = 2)

n=2

A.27160

B.2588

c. 2788

D.988

25E. 22

8. Determine the limit of each sequence if it converges, or say 'div' if otherwise.

P. {In(2n) - In(n)}

{(5n - I)!}

Q. (5n - 3)!

R. {(In n)lO}o/ri

A. In2, 0, 0 B. In 2, 0, div C. In 2, div, 0

D. div, 0, 0 E. 1, 0, div

9. Which of the following series converge?

P. t,nsin (~3)Q ~ 1 .2. ~n3/2sm n

n=8

A. P only

D. R only

B. Q only

E. Q and R only

C. P andQ only


4A

10. Apply the root test to determine if each of the series below converges(C), diverges(D) orif the test is incondusive(I).

00

P. I)V'2 -Itn=7

00 3n2 - 1Q. L 1- 7n - 3n2

n=8

A. P(D), Q(D), R(I)

D. P(C), Q(D), R(C)

B. P(C), Q(I), R(C)

E. P(C), Q(C), R(I)

C. P(C), Q(I), R(I)

11. For which of the following series is the ratio test inconclusive?

00 nA. '"' ~c: sn

n=5

Loo 1· 3· s .. ·(2n + 1)B. nnn=8

00 ,

C. '"' n~c: enn=3

00 2

D '"' n. Z:: n7 + 1n=8

00

E '"' n. ~ (n+ I)!


SA

. 00 112. Find the sum of the seriesL--

n=3 n(n + 1)"

A. 11

B. -2

c. 01

D.3

E. diverges

. 2:00 n 2 . 5 . 8 ... (3n - 1)Use the senes (-1) to answer the next two questions·2n. n! .n=5 """-.~~~~~~~;=~-

13. Evaluate lim Ian+11·n~oo an

A. ~2

2B. 3 c. 2 D. ~

2E. 0

14. Which statements below is correct?

A. The series converges absolutely by the ratio test

B. The series diverges by the ratio test

c. The series converges by the limit comparison test

D. The series diverges by the limit comparison test

E. There is not enough information

#15 - #17 are bonusworth 1 point each

15. According to the alternating series estimation theorem, what is the smallest bound on.001

the error committed by using 87, the 7th partial sum of 2:(-It n2 to approximate then=l

sum of the series?

1A. 62

1B. 27

1C. 82


-------------- -

6A

00 N . 116. Let s = L an and the partial sum SN = Lan = 3 - N!· Find a3+ a4·

n=l n=l

A.76

11B. 24

5c. 12

17. Which of the following series diverges?

00

A. Ln-Sin3n=5

B 00 cos (~).L n2+4nn=5

~e~c. Li2"n=5 n

End of Multiple Choice problems

MAC2312 - Spring 2017 - EXAM2

7A

Section # UFID NAME _On my honor, I have neither given nor received unauthorized aid doing this exam.

FR ScoresSignature: _

I. Find the sum of the series t, [cos (n: 1) - cos (~) 11 /8

2(1) /52(II) /9

SHOW ALLWORK TO RECEIVE FULL CREDIT.

II FR Total I /2211

(a) First, find the Nth partial sum SN. (show all your work)

SN = _

(b) What is the limit of the N -th partial sum SN.

lim SN = _N---+oo

(c) The sum of the series is ... Sum = _


8A

00 3_ (-l)n2. Determine if the seriesL convergesor diverges.

nn=5

(a) Which test did you use? _

(b) Show your work in determining whether the series convergesor diverges.

(c) The series (converges, diverges). (circle one of the choices)

3. Determine if the series f: ~~)n converges absolutely, ,conditionally or diverges.n=5 n nn

(a) Which testes) did you use? --'--_

(b) Show your work.

(c) The series (converges absolutely, converges conditionally, diverges). (circle one)


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