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Cal 2
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PRINTABLE VERSIONPractice Test 1
You scored 100 out of 100Question 1
Your answer is CORRECT.
Evaluate the limit: .
a)
b) 0
c) does not exist
d)
e)
Question 2
Your answer is CORRECT.Give the values of A and B for the function to be continuous at both x = 1 and x = 7.
a) A = 28 and B = 3
b) A = 28 and B = 4
c) A = 27 and B = 4
d) A = 28 and B = 5
e) A = 29 and B = 4
Question 3
( )limx→−5
x − 8− 3 x − 40x2 −13
−113
113
f(x)
f(x) =⎧⎩⎨
Ax − B
24x
B − Ax2
x ≤ 11 < x < 7x ≥ 7
Your answer is CORRECT.
=
a)
b) 1
c) 0
d)
e) The limit does not exist.
Question 4
Your answer is CORRECT.Given , which of the following expressions will represent the first step when finding f ' (x) using the definition of derivative?
a)
b)
c)
d)
e)
f) none of these.
Question 5
Your answer is CORRECT.
Suppose that is a differentiable function, , and . Find given that
limx→0
2 x
cot(4 x)
2
12
f(x) = 3 − 2x2 x√
limh→0
3 − 2(x + h)2x + h− −−−−√
h
limh→0
(3 − 2 ) − (3 − 2 )(x + h)2x + h− −−−−√ x2 x√
h
limh→0
(3 − 2 + h) − (3 − 2 )x2 x√ x2 x√h
limx→h
(3 − 2 ) − (3 − 2 )(x + h)2x + h− −−−−√ x2 x√
h
(3 − 2 ) − (3 − 2 )(x + h)2x + h− −−−−√ x2 x√
h
f f(−2) = 3 (−2) = 4f ′ (−2)g ′
√
.
a)
b)
c)
d)
e)
Question 6
Your answer is CORRECT.
Find A and B given that the function has a minimum value of 32 at .
a) A = 128 and B = 8
b) A = 128 and B = 4
c) A = 64 and B = 12
d) A = 64 and B = 4
e) A = 64 and B = 8
Question 7
Your answer is CORRECT.
The function is invertible. Find given that .
a)
b)
c)
g(x) = 2 f(x) + 2− −−−−−−√
6√
3 5√
5√5
4 5√5
6√6
y = + BA
x√x√ x = 16
f(x) ( )( )f −1′ 5π
2f(x) = 5 x + cos(x)
−14
12
18
d)
e)
Question 8
Your answer is CORRECT.
The function is invertible. Find given that .
a)
b)
c)
d)
e)
Question 9
Your answer is CORRECT.The graph of f is given below. If f is twice differentiable, then which of the following is true?
−12
14
f(x) (257)( )f −1′
f(x) = 4 + 1x3
384
196
192
−1
192
1192
a) f '' (4) < f (4) < f ' (4)
b) f ' (4) < f (4) < f '' (4)
c) f (4) < f ' (4) < f '' (4)
d) f (4) < f '' (4) < f ' (4)
e) f '' (4) < f ' (4) < f (4)
Question 10
Your answer is CORRECT.
Find the slope of the tangent line to at the point where .
a)
b)
c)
d)
f(x) = e2 +4 xx2x = 0
14
−14
4
−4
e)
Question 11
Your answer is CORRECT.
The graph of is shown below. Which of the following could represent the graph of ?
a)
0
(x)f ′ f(x)
b)
c)
d)
Question 12
Your answer is CORRECT.
Which of the following is true about the graph of ?
a) is increasing on the interval .
b) has a local minimum at the point .
c) has a point of inflection at the point .
d) is concave down on the interval .
e) has a vertical asymptote at .
Question 13
Your answer is CORRECT.
Give the derivative of .
a)
f(x) = 27 + − 2x2 54x
f(x) (−∞, 0)
f(x) (1, 79)
f(x) (0, −2)
f(x) (0, ∞)
f(x) x = 54
f(x) = at the point where x =earcsin(4 x) 18
4 3√3
eπ/6
b)
c)
d)
e)
Question 14
Your answer is CORRECT.
An object moves along a coordinate line, its position at each time is given by . Find
the velocity at time
a)
b)
c)
d)
e)
Question 15
Your answer is CORRECT.A 13foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from thewall at the rate of 3 feet per second, at what rate is the area of the triangle formed by the wall, the ground,and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 5 feet from thewall?
a)
b)
c)
8 3√3
eπ/6
2 3√3
eπ/3
2
8
t ≥ 0 x(t) =3 t
2 t + 2= 4.t0
154
350
38
65
16
−1198
11916
1198
d)
e)
Question 16
Your answer is CORRECT.Determine if the function satisfies the Mean Value Theorem on [1, 16]. If so, find allnumbers c on the interval that satisfy the theorem.
a)
b)
c)
d) The Mean Value Theorem does not apply to this function on the given interval.
e)
Question 17
Your answer is CORRECT.
Calculate the indefinite integral: .
a)
b)
c)
d)
e)
Question 18
Your answer is CORRECT.
1194
−1194
f(x) = 3 − 3 xx√
c =252
c = −254
c =258
c =254
∫ dx6 − 3x3
x2
2 − 3x + Cx3
6x + + C3x
3 + + Cx2 3x
18 − + C12 − 6x3
x3
3 − 3x + Cx2
a)
b)
c)
d)
e)
Question 19
Your answer is CORRECT.
a)
b)
c)
d)
e)
Question 20
Your answer is CORRECT.
Given that calculate .
a)
b)
∫ dx =ln(3 )x3
x
9 ln(3 ) + Cx2 x3
+ C1
ln(3 )x3
+ C(ln(3 ))x3 2
18
+ C(ln(3 ))x3 2
6
+ C3
ln(3 )x3
∫ dx =1
2 (5 + )x√ x√
−2 ln(2 ) + Cx√
−2 ln(1 + ) + Cx√
− ln(5 + ) + Cx√
ln(5 + ) + Cx√
− ln(2 ) + Cx√
F (x) = dt∫ 0
x
+ 36t2− −−−−−√ (x)F ′′
0
−6
c)
d)
e)
Question 21
Your answer is CORRECT.
The function is differentiable and Determine the value of .
a)
b)
c)
d)
e)
Question 22
Your answer is CORRECT.
For what values of is the following equation true?
a)
b)
c)
d)
e)
Question 23
Your answer is CORRECT.
− + 36x2− −−−−−√
x
+ 36x2− −−−−−√
−x
+ 36x2− −−−−−√
f (3 f(t) + 3 t) dt = sin(x).∫ x
0( )f ′ π
6
−3√
6π
6
0
3√2
1
−76
k 5 x dx = 0∫ k
−1
{−1, 0, 1}
{−1, 1}
0
1
−1
Given that .
a)
b)
c)
d)
e)
Question 24
Your answer is CORRECT.
Calculate:
a)
b)
c)
d)
e)
f(x) dx = 1, f(x) dx = 4 and f(x) dx = 6 find f(x) dx∫ 4
1∫ 4
2∫ 5
1∫ 5
2
−9
−5
9
11
7
6 dx∫ 0
−2x2(2 + 1)x3
2
67523
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