Deck 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Question 1

Find the limit.

Answer 1

Question 2

Simplify the expression.

A)
B)
C)
D)
E)

Answer 2

Question 3

Evaluate the limit using l'Hôpital's Rule.

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

Answer 3

( $\infty$ )

Question 4

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 5

Find the numerical value of the expression.

A)
B)
C)
D)
E)

Question 6

Find the derivative.

A)
B)
C)
D)
E)

Question 7

Find the derivative of the function. Simplify where possible.

A)
B)
C)
D)
E)

Question 8

Evaluate the limit using l'Hôpital's Rule.

A)
B)3
C)0
D)

Question 9

Find the exact value of the expression.

A)
B)
C)
D)
E)

Question 10

If is invested at interest, find the value of the investment at the end of years if the interest is compounded .

A)
B)
C)
D)
E)

Question 11

Find the value of the expression accurate to four decimal places.sinh 4

A)29.3082
B)55.5798
C)15.145
D)27.2899

Question 12

Find the numerical value of the expression.

A)
B)
C)
D)
E)

Question 13

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

A)
B)
C)
D)
E)

Question 14

Differentiate the function.

A)
B)
C)
D)

Question 15

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

A)
B)
C)
D)
E)

Question 16

Evaluate the limit using l'Hôpital's Rule.

A)75
B)25
C)15
D)

Question 17

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

A)
B)
C)
D)
E)

Question 18

Find the limit.

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

Question 19

If is invested at interest, find the value of the investment at the end of years if the interest is compounded .

A)
B)
C)
D)
E)

Question 20

Find the exact value of the expression.

A)
B)
C)
D)
E)

Question 21

Use logarithmic differentiation to find the derivative of the function.

A)
B)
C)
D)

Question 22

Starting with the graph of , find the equation of the graph that results from reflecting about the line .

A)
B)
C)
D)
E)

Question 23

When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by (The maximum charge capacity is and t is measured in seconds.) How long does it take to recharge the capacitor to 90% of capacity if ?

A) seconds
B) seconds
C) seconds
D) seconds
E) seconds

Question 24

Starting with the graph of , write the equation of the graph that results from shifting 5 units right.

A)
B)
C)
D)
E)

Question 25

Find .

A)
B)
C)
D)
E)

Question 26

If , find .

A)
B)
C)
D)
E)

Question 27

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 28

Differentiate the function.

Question 29

Solve the equation.

A)x = ln + 2
B)x = ln - 2
C)x = ln + 2
D)x = ln - 2

Question 30

Use logarithmic differentiation to find the derivative of the function.

A)
B)
C)
D)
E)

Question 31

Find an equation of the tangent line to the curve at .

Question 32

Suppose that the graph of is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

A)13,014,952 mi
B)13015052.4 mi
C)5.2 mi
D)13,015,152 mi
E)1084587.7 mi

Question 33

Determine whether f is one-to-one.

Question 34

Find the domain, range, and x-intercept(s) of the function.

Question 35

The graph of f is given. Sketch the graph of on the same set of axes. 3

Question 36

Solve each equation for x.(a) (b)

Question 37

Differentiate the function.

Question 38

Find the exact value of the expression.

A)2
B)4
C)1
D)5
E)3

Question 39

Find a formula for the inverse of the function.

A)
B)
C)
D)
E)

Question 40

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 41

Find the limit.

A)
B)
C)
D)
E)

Question 42

Find the exponential function whose graph is given.

A)
B)
C)
D)
E)

Question 43

Find the limit.

A)
B)
C)
D)
E)