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Calculus II - Test 1 with Solution Key - Fall 2016 | MATH 1432, Exams of Calculus

Material Type: Exam; Class: Calculus II; Subject: (Mathematics); University: University of Houston; Term: Spring 2016;

Typology: Exams

2015/2016

Uploaded on 05/09/2016

nguyencaoduyenanh
nguyencaoduyenanh 🇺🇸

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5/9/2016 PrintTest
https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 1/10
PRINTABLEVERSION
Test1
Youscored100outof100
Question1
YouranswerisCORRECT.
Evaluate:
a)
b)
c)
d)
e) doesnotexist
Question2
YouranswerisCORRECT.
Evaluate:
a)
b) doesnotexist
c)
d)
e)
lim
x
1
16
x
2
x
+ 1
0
3
5
1
3
x
0
(7
x
)
sin
2
3
x
2
49
3
3
49
0
49
9
pf3
pf4
pf5
pf8
pf9
pfa

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Download Calculus II - Test 1 with Solution Key - Fall 2016 | MATH 1432 and more Exams Calculus in PDF only on Docsity!

PRINTABLE VERSION

Test 1

You scored 100 out of 100

Question 1

Your answer is CORRECT.

Evaluate:

a)

b)

c)

d)

e) does not exist

Question 2

Your answer is CORRECT.

Evaluate:

a)

b) does not exist

c)

d)

e)

lim x→−

x^2 − 16 x + 1

lim x→

sin^2 (7x) 3 x^2

Question 3

Your answer is CORRECT.

Give the value of in the interval that satisfies the conclusion of the mean value theorem for .

a)

b)

c)

d)

e)

Question 4

Your answer is CORRECT.

The function is defined everywhere except at. If possible, define at

so that it becomes continuous at.

a)

b)

c) Not possible because there is an infinite discontinuity at the given point.

d) Not possible because there is a jump discontinuity at the given point.

e)

Question 5

Your answer is CORRECT.

An object moves along the axis and its position is given by the function

. Find the acceleration at time.

a)

c [0, 2] g(x) = − √x+ 4

f(x) =

x + 2 x^2 − 4

x = ±2 f

x = −2 x = −

f(−2) = −

f(−2) = −

f(−2) = 0

x s(t) = t^3 − 6 t^2 + 4t + 6 t = −

e)

Question 8

Your answer is CORRECT.

Find the slope of the tangent line to at the point where.

a)

b)

c)

d)

e)

Question 9

Your answer is CORRECT.

The graph of (the derivative of ) is shown below. At what value of does the graph of change from decreasing to increasing? You may assume that the x intercepts are all integers.

f(x) = e^2 x +3^ x

2 x = 0

f ′^ f x f(x)

a)

b)

c)

d)

Question 10

Your answer is CORRECT.

Evaluate the limit:

a)

b)

c)

d)

e) does not exist

Question 11

Your answer is CORRECT.

The function is differentiable, and the tangent line to the graph of at

. Let Give.

a)

b)

c)

d)

e)

lim h→

( (6 + h)^2 − (6 + h)) − ( 62 − 6)

h

g y = g(x) x = −5 is y = 3x − 2 f(x) = 2g(x) + 4x + 3. f ′(−5)

a)

b)

c)

d)

e)

Question 14

Your answer is CORRECT.

Determine the interval(s) at which is concave down.

a) (–∞, –3), (2, ∞)

b) (–2, ∞)

c) (–2, 3)

d) (–∞, –2), (3, ∞)

e) (–∞, 3)

Question 15

Your answer is CORRECT.

A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1080 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area.

a) by^ feet with the divider^ feet long

b) by^ feet with the divider^ feet long

c) by^ feet with the divider^ feet long

d) by^ feet with the divider^ feet long

e) by feet with the divider feet long

Question 16

Your answer is CORRECT.

f(x) = − + + 9 + 2x + 7

x^4

x^3 x^2

A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 24 cm to 17 cm in 30 minutes. At what rate, in cubic cm per minute, is the volume of the snowball changing at the instant the radius is 1 cm?

a)

b)

c)

d)

e)

Question 17

Your answer is CORRECT.

Use the graph of below to find.

136 π 15

28 π 15

7 π

14 π 15

7 π 15

f(x) ∫ f(x) dx

7

e)

Question 20

Your answer is CORRECT.

Calculate:

a)

b)

c)

d)

e)

f(x) = + + 2x

x^6

x^5

∫ dx

ex 1 + 36 e^2 x

arctan(6 ) + C

ex

6 arcsin(6 ex) + C

arctan(6 ) + C

ex

6 arctan(6 ex) + C

arcsin(6 ) + C

ex