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MAT 266 Test 2 Answers, Exams of Calculus

The answers to Test 2 of MAT 266 course at ASU. The test consists of 14 questions worth a total of 60 points, with questions 1-10 being multiple choice and questions 11-14 being free response. The topics covered in the test include finding areas and volumes of regions, evaluating integrals, and calculating work. The document also includes an honor statement that confirms the student has not given or received any unauthorized assistance on the exam.

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2021/2022

Uploaded on 05/11/2023

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MAT 266 Test2
1
Directions:
1. There are 14 questions worth a total of 60 points.
2. Questions 1 - 10 are Multiple Choice worth 4 points each to be answered on
the supplied SCANTRONS.
3. Questions 11 - 14 are Free Responses worth 5 points each and are to be
answered in the space provided on the test.
4. Read all the questions carefully.
5. For the Free Response, you must show all work in order to receive credit!!
6. When possible, box your answer, which must be complete, organized, and
exact unless otherwise directed.
7. Always indicate how a calculator was used (i.e. sketch graph, etc. …).
8. No calculators with QWERTY keyboards or ones like TI-89 or TI-92 that
do symbolic algebra may be used.
Honor Statement:
By signing below you confirm that you have neither given nor received any unauthorized assistance
on this exam. This includes any use of a graphing calculator beyond those uses specifically
authorized by the Mathematics Department and your instructor. Furthermore, you agree not to
discuss this exam with anyone until the exam testing period is over. In addition, your calculator’s
program memory and menus may be checked at any time and cleared by any testing center proctor
or Mathematics Department instructor.
_______________________________________ _________________
Signature Date
MAT 266
TEST 2 - ANSWERS
SoMSS, ASU
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Download MAT 266 Test 2 Answers and more Exams Calculus in PDF only on Docsity!

Directions:

1. There are 14 questions worth a total of 60 points.

2. Questions 1 - 10 are Multiple Choice worth 4 points each to be answered on

the supplied SCANTRONS.

3. Questions 11 - 14 are Free Responses worth 5 points each and are to be

answered in the space provided on the test.

4. Read all the questions carefully.

5. For the Free Response, you must show all work in order to receive credit!!

6. When possible, box your answer, which must be complete, organized, and

exact unless otherwise directed.

7. Always indicate how a calculator was used (i.e. sketch graph, etc. …).

8. No calculators with QWERTY keyboards or ones like TI-89 or TI-92 that

do symbolic algebra may be used.

Honor Statement:

By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone until the exam testing period is over. In addition, your calculator’s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor.

_______________________________________ _________________

Signature Date

MAT 266

TEST 2 - ANSWERS

SoMSS, ASU

  1. Find the area of the region bounded by the curves y = x^2^ − 2 x & y = x + 4. Select the correct answer. a.

b. 25 3 c. 20 d.

e. None of these

  1. Find the volume of the solid obtained by rotating the region bounded by y = x^2 and x = y^2 about the x -axis. Select the correct answer. a. 5

6 π (^) b. 10

3 π (^) c. 5

(^2) d. 5

π (^) e. None of these

  1. Which of the following integrals is equal to 1.25? Select the correct answer.

a.

1

0

(^1) dx ∫ (^) x b.

1

0

(^1) dx ∫ (^) x c.

1

0

(^1) dx ∫ (^) x d.

1 2 0

(^1) dx ∫ (^) x e. none of these

  1. A spring has a natural length of 22 cm. If a force of 15 N is required to keep it stretched to a length of 32 cm, how much work is required to stretch it from 22 cm to 40 cm? Select the correct answer. a. 3.43 J b. 1.93 J c. 2.43 J d. 3.93 J e. None of these
  2. Find lim(3 n →∞ + e −^2 n ) Select the correct answer a. 3 b. 0 c. 4 d. 2 e. None of these
  3. A rope, 40 ft long, weighs 0.8 lb/ft and hangs over the edge of a building 110 ft high. How much work is done in pulling the rope to the top of the building? Select the correct answer. a. 640 ft-lb b. 590 ft-lb c. 641 ft-lb d. 489 ft-lb e. None of these
  4. Find the sum of the series 4

n

n

∑ Select the correct answer

a.

b.

c.

d.

e. None of these

Answer: d

Answer: b

Answer: c

Answer: c

Answer: a

Answer: a

Answer: b

  1. The tank shown is full of water. Given that water weighs work required to pump the water out of the tank.

Solution: Volume of the ith^ element =

Weight of the ith^ element = 62.5 (25 )

Work done to pump out the ith

Work done to pump out all the water

  1. Evaluate the integral or

Solution:

First observe

∫ (^) x (ln x ) ∫

So,

2 2 = lim[ ]

= lim[ ]

x x x x

∞ ∫ ∫

FREE RESPONSE

The tank shown is full of water. Given that water weighs 62.5 lb/ft^3 work required to pump the water out of the tank.

element = π (25 − xi^2 )∆ x 62.5 (25 2 ) π − xix element = 62.5 π (25 − xi^2 ) xix

Work done to pump out all the water = ith^ element =

5 2 0

∫^ 62.5^ π^ (25^ −^ x^ )^ xdx^ =^ 9765.625π ft^ − lb

or show that it is divergent: (^4) 2

(ln )

dx x x

∞ ∫.

4 4

3

(^1) ( ln ) (ln ) 1 3[ln ]

dx u du u x x x

x

∫ ∫

4 4 2 2

3 2

3 3 3

(^1) lim 1 (ln ) (ln ) 1 = lim[ ] 3(ln )

= lim[ 1 1 ]^1 3(ln ) 3(ln 2) 3(ln 2)

t t x t t x

t

dx dx x x x x

x

t

→∞

→∞ =

→∞

∫ ∫

62.5 lb/ft 3 and R = 5 ft, find the

62.5 π (25 − x ) xdx = 9765.625π ftlb

  1. Set up the integral for the volume of the solid obtained by rotating the region bounded by y = x^3 and x = y^3 in the first quadrant, about the line x =− 1. ( Do not evaluate the integral )

Solution: Outer radius of the cross-section = y 1/3^ + 1 Inner radius of the cross-section = y^3 + 1

Volume =

1 1/3 2 3 2 0

π (^) ∫ [( y + 1) − ( y +1) ] dy

  1. The height of a monument is 20 m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side x /4 meters. Find the volume of the monument.

Solution:

The height of an equilateral triangle with side-length equal to s units =

s

So, area of the equilateral triangle = 1 3 3 2 2 2 4

ss = s

For our problem, area of the equilateral triangle = 3 2 64

x

Hence, volume of the monument =

20 2 0

∫^ x^ dx^ =