Deck 5: Integrals

Question 1

Evaluate the limit using l'Hôpital's Rule.

A) 25
B) 15
C) 0
D) 75

Answer 1

75

Question 2

Find the numerical value of the expression

A)
B)
C)
D)
E)

Answer 2

Question 3

If $5000 is invested at 3% interest,find the value of the investment at the end of 5 years if the interest is compounded .

A)
B)
C)
D)
E)

Answer 3

Question 4

The half-life of cesium -137 is 30 years.Suppose we have a 150-mg sample.Find the mass that remains after years.

A)
B)
C)
D)
E)

Question 5

Strontium-90 has a half-life of 28 days.A sample has a mass of 50 mg initially.Find a formula for the mass remaining after days.

A)
B)
C)
D)
E)

Question 6

________

A)
B)
C)
D)
E)

Question 7

Find the derivative.

A)
B)
C)
D)
E)

Question 8

Find the limit.

A)
B)
C) 0
D)
E) 1

Question 9

Find the numerical value of the expression

A)
B)
C)
D)
E)

Question 10

If $5000 is invested at 8% interest,find the value of the investment at the end of 4 years if the interest is compounded monthly.

A)
B)
C)
D)
E)

Question 11

Evaluate the limit using l'Hôpital's Rule.

A)
B) 3
C)
D) 0

Question 12

Find the derivative of the function.Simplify where possible

A)
B)
C)
D)
E)

Question 13

Evaluate the expression. (a) (b)

A)
B)
C)
D)
E)

Question 14

Simplify the expression.

A)
B)
C)
D)
E)

Question 15

The half-life of cesium-137 is 30 years.Suppose we have a 170-mg sample.How much of the sample remains after 140 years?

A)
B)
C)
D)
E)

Question 16

A telephone line hangs between two poles at 12 m apart in the shape of the catenary , where x and y are measured in meters.Find the slope of this curve where it meets the right pole.

A)
B)
C)
D)
E)

Question 17

Find the exact value of the expression

A)
B)
C)
D)
E)

Question 18

Evaluate the limit using l'Hôpital's Rule.

A) 0
B) 1
C) e
D) ( $\infty$ )

Question 19

Find the exact value of the expression

A)
B)
C)
D)
E)

Question 20

Find the limit.

Question 21

The acceleration function (in m/ )and the initial velocity are given for a particle moving along a line.Find the velocity at time t and the distance traveled during the given time interval.

A)
B)
C)
D)
E)

Question 22

Use the laws of logarithms to write the expression as the logarithm of a single quantity. 4 ln 5 - ln (x + 6)

A)
B)
C)
D)

Question 23

Evaluate the integral.

A)
B)
C)
D)
E)

Question 24

Find a formula for the inverse of the function.

A)
B)
C)
D)
E)

Question 25

Find an equation of the tangent line to the curve at (1 , 0)

Question 26

Assume that is a one-to-one function.
(a)If ,what is ?
(b)If ,what is ?

A)
B)
C)
D)
E)

Question 27

If ,find .

A) 4
B) 2
C) 12
D) 6
E) 16

Question 28

Differentiate the function.

Question 29

Use the laws of logarithms to expand the expression. ln

A) ln
B) ln (x + 5)- ln (x - 6)
C) ln [(x + 5)(x - 6)]
D) ln

Question 30

Use the laws of logarithms to expand the expression. ln

A) ln
B) ln (x + 5)- ln (x - 6)
C) ln [(x + 5)(x - 6)]
D) ln

Question 31

Differentiate the function

A)
B)
C)
D)
E)

Question 32

Find a formula for the inverse of the function.

A)
B)
C)
D)
E)

Question 33

The velocity function (in meters per second)is given for a particle moving along a line.Find the distance traveled by the particle during the given time interval.

A) 68 m
B) 100 m
C) 64 m
D) 36 m
E) 72 m

Question 34

Find the exponential function whose graph is given.

A)
B)
C)
D)
E)

Question 35

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure)is given by the integral https://d2lvgg3v3hfg70.cloudfront.net/TB2067/.Find the area..

A)
B)
C)
D)
E)

Question 36

Use logarithmic differentiation to find the derivative of the function.

A)
B)
C)
D)

Question 37

Evaluate the integral.

A)
B)
C)
D)
E)

Question 38

Differentiate the function.

A)
B)
C)
D)

Question 39

Evaluate the integral.

A)
B)
C)
D)
E)

Question 40

Find

A)
B)
C)
D)
E)

Question 41

The graph of f is given.Sketch the graph of on the same set of axes.