MA 166: Spring 2000 Final Exam in Calculus, Exams of Analytical Geometry and Calculus

The final exam for ma 166 calculus course held in spring 2000. The exam consists of 25 multiple-choice problems covering various topics in calculus such as limits, derivatives, integrals, and series.

Typology: Exams

2012/2013

Uploaded on 02/12/2013

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MA 166 FINAL EXAM Spring 2000 Page 1/10
NAME
STUDENT ID #
RECITATION INSTRUCTOR
RECITATION TIME
LECTURER
INSTRUCTIONS
1. There are 10 different test pages (including this cover page). Make sure you have a
complete test.
2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social security
number). Also write your name at the top of pages 2–10.
3. Do any necessary work for each problem on the space provided or on the back of
the pages of this test booklet. Circle your answers in this test booklet. No partial
credit will be given, but if you show your work on the test booklet, it may be used in
borderline cases.
4. No books, notes or calculators may be used on this exam.
5. Each problem is worth 8 points. The maximum possible score is 200 points.
6. Usinga#2pencil
, fill in each of the following items on your answer sheet:
(a) On the top left side, write your name (last name, first name), and fill in the little
circles.
(b) On the bottom left side, under SECTION, write in your division and section
number and fill in the little circles. (For example, for division 9 section 1, write
0901. For example, for division 38 section 2, write 3802).
(c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your
student ID number, and fill in the little circles.
(d) Using a #2 pencil, put your answers to questions 1–25 on your answer sheet by
filling in the circle of the letter of your response. Double check that you have filled
in the circles you intended. If more than one circle is filled in for any question,
your response will be considered incorrect. Use a #2 pencil.
7. After you have finished the exam, hand in your answer sheet and your test booklet to
your recitation instructor.
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MA 166 FINAL EXAM Spring 2000 Page 1/

NAME

STUDENT ID

RECITATION INSTRUCTOR

RECITATION TIME

LECTURER

INSTRUCTIONS

  1. There are 10 different test pages (including this cover page). Make sure you have a complete test.
  2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social security number). Also write your name at the top of pages 2–10.
  3. Do any necessary work for each problem on the space provided or on the back of the pages of this test booklet. Circle your answers in this test booklet. No partial credit will be given, but if you show your work on the test booklet, it may be used in borderline cases.
  4. No books, notes or calculators may be used on this exam.
  5. Each problem is worth 8 points. The maximum possible score is 200 points.
  6. Using a #2 pencil, fill in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, first name), and fill in the little circles. (b) On the bottom left side, under SECTION, write in your division and section number and fill in the little circles. (For example, for division 9 section 1, write
  7. For example, for division 38 section 2, write 3802). (c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your student ID number, and fill in the little circles. (d) Using a #2 pencil, put your answers to questions 1–25 on your answer sheet by filling in the circle of the letter of your response. Double check that you have filled in the circles you intended. If more than one circle is filled in for any question, your response will be considered incorrect. Use a #2 pencil.
  8. After you have finished the exam, hand in your answer sheet and your test booklet to your recitation instructor.
  1. Consider the triangle ABC with vertices A = (0, 0 , 0), B =

x, x 2 , 0

, and C = (1, 2 , 0), where x > 0. If the area of the triangle is 6, then x = A. 4 B. 8 C. 3 D. 5 E. 2

  1. Let ~a = ~i + ~j + ~k and ~b = ~i + x~j, where x > 0. Find x so that ‖pr~a~b‖ = 1.

A. 2 B.

C. 3

D.

E.

  1. lim x→ 0

x sin x 1 − cos^3 x

A.

B. −

C. 0

D. 1

E. does not exist

1

1 + x^2 dx =

A. π 2 B. integral diverges C. π D. π 3 E. π 4

1

x ln xdx =

A. 2 ln 2 −

B. ln 2 −

C.

ln 2 −

D.

E. 2 ln 2 −

2

x^2 − 1

dx =

A.

ln 3

B. ln

C. ln

D.

ln

E. ln 3

  1. Let R be the region between the graph of y = sin x and the x-axis on the interval [0, π]. The volume of the solid obtained by revolving R about the x-axis is

A. π 2 B. π^2 C. π

D. π^2 2

E. π^2 3

  1. The length of the graph of f (x) = 5 +

x (^32) , 0 ≤ x ≤ 2, is equal to

A. 3

B.

C.

D. 2

E. 3

  1. Suppose that a force of 4 lbs is required to stretch a spring 2 ft beyond its natural length. How much work is required to stretch it from 2 ft to 3 ft beyond its natural length? A. 9 ft-lbs B. 4 ft-lbs C. 6 ft-lbs D. 5 ft-lbs E. 2 ft-lbs
  1. Which of the following series converge?

(I)

∑^ ∞

n=

(−1)n^ ln n n

(II)

∑^ ∞

n=

cos

n

(III)

∑^ ∞

n=

n^2 2 n

A. (II) and (III) only B. (III) only C. (I) and (II) only D. (I) only E. (I) and (III) only

  1. Which of the following series converge absolutely?

(I)

∑^ ∞

n=

(−1)n^

n

(II)

∑^ ∞

n=

cos n n^2

(III)

∑^ ∞

n=

(−1)n^

n^3 + 1

A. (II) and (III) only B. (III) only C. (I) and (II) only D. (I) only E. (I) and (III) only

  1. The series

∑^ ∞

n=

3 n 7 n+

A. diverges

B. = 143

C. = 12

D. = 37

E. = 47

  1. The series

∑^ ∞

n=

ln n + 3n A. converges by comparison with

∑^ ∞

n=

ln n

B. diverges by comparison with

∑^ ∞

n=

ln n

C. converges by comparison with

∑^ ∞

n=

3 n

D. diverges by comparison with

∑^ ∞

n=

3 n E. diverges by the ratio test

  1. The radius of convergence of the power series

∑^ ∞

n=

n^2 n!

xn^ is (^) A. e

B.

e C. 1 D. ∞ E. 2

  1. Use the Taylor series of e−x 3 to approximate

0

e−x

3 dx with error less than 0.01. The smallest number of terms of the series that are needed for this accuracy is A. 2 B. 3 C. 4 D. 5 E. 6

  1. The length of the parametrized curve

x =

t^3 , y =

t^2 + 3, 0 ≤ t ≤ 1

is A. 2

B.

C.

D.

E. (

  1. In the Taylor series of f (x) =

x about a = 2, the coefficient of (x − 2)^3 is

A. −

B.

C. −

D. −

E. −