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