test 1
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Cal 2TRANSCRIPT
PRINTABLE VERSIONTest 1
You scored 100 out of 100Question 1
Your answer is CORRECT.
Evaluate:
a)
b) does not exist
c)
d)
e)
Question 2
Your answer is CORRECT.
Evaluate:
a)
b)
c)
d)
e) does not exist
Question 3
Your answer is CORRECT.
limx→1
− 16x2
x − 1
−5
13
0
−3
limx→0
tan(7x)5x
57
0
4925
75
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.Suppose that for a function is not defined. Also suppose that
. Which, if any, of the following statements is false?
a)
b) f has infinite discontinuity at x = 3
c) If we redefine f so that f(3) = 4 then the new function will be continuous at x = 3
d) f has removable discontinuity at x = 3
e) All of the above statements are true.
Question 5
Your answer is CORRECT.
An object moves along the axis and its position is given by the function . Findthe acceleration at time .
a)
b)
c)
c [0, 5]g(x) = −2 − 2x√
34
74
94
54
1
f, f(3)f(x) = −4 and f(x) = −4lim
x→3−lim
x→3+
f(x) = −4limx→3
x s(t) = − 4 + 3t + 5t3 t2
t = −2
0
−20
31
d)
e)
Question 6
Your answer is CORRECT.
Let be a polynomial function such that . Classify the point .
a) local maximum
b) inflection point
c) local minimum
d) intercept
e) none of the these
Question 7
Your answer is CORRECT.
Suppose f(x) is an invertible differentiable function and . Find .
a)
b)
c)
d)
e)
Question 8
Your answer is CORRECT.
Find the slope of the tangent line to at the point where .
6
−25
f(x) f(3) = −3, (3) = 0 and (3) = 4f ′ f ′′
(3, −3)
f(3) = 4, f(4) = −2, (3) = −3, (−2) = 1f ′ f ′
(4)( )f −1′
3
−13
13
−3
1
f(x) = e4 +2 xx2x = 0
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 changefrom increasing to decreasing? You may assume that the xintercepts are all integers.
a)
b)
c)
d)
Question 10
0
2
12
−12
−2
f ′ f x f(x)
0
−3
2
4
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)
Question 12
Your answer is CORRECT.
Find the equation of the tangent line to the curve at the point .
a)
b)
c)
d)
limh→0
−2 + h− −−−−√ 2√
h
0
2 2√
2√4
2√2
g y = g(x) x = 5 is y = 3x − 4f(x) = −2g(x) + 4x + 1. (5)f ′
3
−18
−6
−2
11
4 + 2 − 5 = 2 xy − xx2 y 2 (1, 1)
2 x − 7 y = −5
−7 x + 2 y = 9
7 x + 2 y = −5
−2 x − 7 y = −9
e)
Question 13
Your answer is CORRECT.
The graph of is shown below. Give the smallest value of where the graph of has a pointof inflection.
a)
b)
c)
d)
e)
Question 14
Your answer is CORRECT.
Determine the interval(s) at which is concave down.
a) (–∞, –3), (2, ∞)
7 x + 2 y = 9
y = (x)f ′ x f(x)
4
−3
7
−6
0
f(x) = − + + 9 + 2x + 714
x4 12
x3 x2
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 theplayground. 480 feet of fencing is used. Find the dimensions of the playground that will enclose the greatesttotal 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.A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasingfrom 36 cm to 9 cm in 30 minutes. At what rate, in cubic cm per minute, is the volume of the snowballchanging at the instant the radius is 5 cm?
a)
b)
c)
d)
e)
Question 17
Your answer is CORRECT.
Use the graph of below to find .
130 90 130
115 85 116
120 120 120
120 80 80
140 90 90
675π
−90π
−80π
−180π
45π
f(x) f(x) dx∫ 8
−2
a)
b)
c)
d)
e)
Question 18
Your answer is CORRECT.
Calculate the integral:
a)
b)
c)
d)
19
16
2
0
−2
∫ (8 x sin( ) + 4 tan(x) cos(x) csc(x)) dxx2
−8 cos(x) + 4 x + C
−4 cos( ) + 4 sin(x) + Cx2
4 sin( ) + 4 x + Cx2
−4 cos( ) − 4 cos(x) + Cx2
e)
Question 19
Your answer is CORRECT.
Give a formula for given that is continuous and .
a)
b)
c)
d)
e)
Question 20
Your answer is CORRECT.
Calculate:
a)
b)
c)
d)
e)
−4 cos( ) + 4 x + Cx2
f(x) f 2 + + 1 = dtx4 x2 ∫ x
0
f(t)t + 3
f(x) = 8 + 24 + 2 + 6xx4 x3 x2
f(x) = 8 + 2xx3
f(x) = 2 + + 1x4 x2
f(x) = + + + + + 3x25
x6 65
x5 13
x4 x3 x2
f(x) = + + x25
x5 13
x3
∫ dxex
1 + 36 e2 x
arctan(6 ) + C112
ex
6 arcsin(6 ) + Cex
arctan(6 ) + C16
ex
6 arctan(6 ) + Cex
arcsin(6 ) + C16
ex