prac test 1

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


=

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


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


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


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


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


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


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


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


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


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


Calculate the indefinite integral: .

a)

b)

c)

d)

e)

Question 18


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


a)

b)

c)

d)

e)

Question 20


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


The function is differentiable and Determine the value of .

a)

b)

c)

d)

e)

Question 22


For what values of is the following equation true?

a)

b)

c)

d)

e)

Question 23


− + 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


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

33763

16883

8443

3443

prac test 1

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