Deck 7: Exponentials, Logarithms and Other Transcendental Functions

Question 1

Graph the function.

A)
B)
C)
D)

Answer 1

Question 2

Use the properties of logarithms to rewrite the expression as a single term.

A)
B)
C)
D) ( = 0)

Answer 2

( = 0)

Question 3

Evaluate the limit.

A) 1
B) 0
C)
D) indeterminant

Answer 3

0

Question 4

Evaluate the integral.

A)
B)
C)
D)

Question 5

Evaluate the limit.

A) 1
B) 0
C)
D) indeterminant

Question 6

Evaluate the integral.

A)
B)
C)
D)

Question 7

Evaluate the integral.

A)
B)
C)
D)

Question 8

The gain g of a signal amplifier (an electronics component) is given by , where x is the input signal in millivolts. Find an x that maximizes the gain. Round to three decimal places.

A) 2.718
B) 7.389
C) 1.532
D) 1.763

Question 9

Show that and for all x. Show all work. and

Question 10

Find the derivative of .

A)
B)
C)
D)

Question 11

Use logarithmic differentiation to find the derivative of the given function. .

A)
B)
C)
D)

Question 12

Use logarithmic differentiation to find the derivative of the given function. .

A)
B)
C)
D)

Question 13

Evaluate the integral.

A)
B)
C)
D)

Question 14

Use the properties of logarithms to rewrite the expression as a single term.

A)
B)
C)
D)

Question 15

Find the derivative of .

A)
B)
C)
D)

Question 16

Use Simpson's Rule with n = 4 to estimate ln 3. Round your answer to the nearest tenth.

A) 1.1
B) 3.3
C) 1.3
D) 2.2

Question 17

Express the number as an integral.

A)
B)
C)
D)

Question 18

Graph the function. [It may be helpful to find the intervals on which the function is increasing and decreasing, concave up and concave down.]

A)
B)
C)
D)

Question 19

Use the properties of logarithms to rewrite the expression as a single term.

A)
B)
C)
D)

Question 20

Use the properties of logarithms to rewrite the expression as a single term.

A)
B)
C)
D)

Question 21

Find all extrema and inflection points.

A) extrema at inflection points at
B) no extrema inflection point at
C) extremum at inflection points at
D) extremum at inflection points at

Question 22

Find the derivative of .

A)
B)
C)
D)

Question 23

Decide whether the function described has an inverse. The weight of a package dependent upon the amount of postage bought.

A) yes
B) no

Question 24

Decide whether the function described has an inverse. The length of the shadow of a flagpole from noon to dusk.

A) yes
B) no

Question 25

Evaluate the integral.

A)
B)
C)
D)

Question 26

Assume that the function has an inverse, and, without solving for the inverse, find the indicated value. ;

A)
B)
C)
D)

Question 27

Evaluate the integral exactly.

A)
B)
C)
D)

Question 28

Use the given graph to sketch the inverse function.

A)
B)
C)
D)

Question 29

Find all extrema and inflection points.

A) extremum at inflection points at
B) extrema at and inflection points at
C) extremum at no inflection points
D) extremum at no inflection points

Question 30

Use the given graph to sketch the inverse function.

A)
B)
C)
D)

Question 31

Find the derivative of .

A)
B)
C)
D)

Question 32

Evaluate the integral.

A)
B)
C)
D)

Question 33

Use a graph to determine if the function is one-to-one. If it is, find the inverse and graph both the function and its inverse.

A) one-to-one
B) not one-to-one
C) not one-to-one
D) one-to-one

Question 34

Determine if the function is one-to-one. If it is, then find its inverse and graph both the function and its inverse.

Question 35

Show that and for all x. Show all work. and ;

Question 36

Show that and are inverse functions. Show all of your work.

Question 37

Determine if the function is one-to-one. If it is, then find its inverse and graph both the function and its inverse.

Question 38

Find an equation of the tangent line for at x = 2.

A)
B)
C)
D)

Question 39

Sketch the graph of

A)
B)
C)
D)

Question 40

Assume that the function has an inverse, and, without solving for the inverse, find the indicated value. ;

A)
B)
C)
D)

Question 41

An investment compounded continuously will be worth , where A is the investment in dollars, r is the annual interest rate, and t is the time in years. APY can be defined as , the relative increase of worth in one year. Find the APY for an interest rate of 7%. Express the APY as a percent rounded to 2 decimal places.

A)
B)
C)
D)

Question 42

A bacterial population starts at 200 and quintuples every day. Calculate the percent rate of change rounded to 2 decimal places.

A) 179.18 %
B) 160.94 %
C) 1.61 %
D) 110.94 %

Question 43

Evaluate the integral.

A)
B)
C)
D)

Question 44

Evaluate the inverse functions by sketching a unit circle and locating the correct angle on the circle. (a) (b) (c)

A) (a) (b)
(c)
B) (a) (b)
(c)
C) (a) 0 (b)
(c)
D) (a) 0 (b)
(c)

Question 45

Sketch a graph of the function.

A)
B)
C)
D)

Question 46

Use a triangle to simplify the expression. .

A)
B)
C)
D)

Question 47

A picture hanging in an art gallery has a frame 15 inches high and the bottom of the frame is 6 feet above the floor. A person whose eye is 6 ft above the floor stands x feet from the wall. Let A be the angle formed by the ray from the person's eye to the bottom of the frame and the ray from the person's eye to the top of the frame. Write A as a function of x and graph y = A(x).

A)
B)
C)
D)

Question 48

Sketch the graph of the function.

Question 49

Find the derivative of .

A)
B)
C)
D)

Question 50

Evaluate the integral.

A)
B)
C)
D)

Question 51

Evaluate the integral.

A)
B)
C)
D)

Question 52

Use a triangle to simplify the expression.

A)
B)
C)
D)

Question 53

A flywheel of radius r is driven by a reciprocating shaft S and a linking arm L (see figure below). If x represents the displacement of the shaft from its leftmost position, then the angle between the linking arm and the centerline of the shaft is . Find the maximum value of .

A)
B)
C)
D)

Question 54

Sketch the graph of the function.

Question 55

Find all solutions.

A) or
B) or
C)
D) or

Question 56

Find all solutions.

A)
B)
C)
D)

Question 57

Graph the function.

A)
B)
C)
D)

Question 58

The population of trout in a certain overstocked lake is expected to follow the model ,
where p is the population in thousands and t is the time in months. Show that and use this information to determine that the population model never reaches zero.

Question 59

Evaluate the integral.

A)
B)
C)
D)

Question 60

Find the derivative of the given function.

A)
B)
C)
D)

Question 61

Find the derivative of the function.

A)
B)
C)
D)

Question 62

Evaluate the integral.

A) e^{sinh 4}
B) e^{sinh 4} - 1
C) -e^{sinh 4} - 1
D) -e^{sinh 4}

Question 63

Find the derivative of the function.

A)
B)
C)
D)

Question 64

Suppose that a hanging cable has the shape for . Find the length of the cable.

A)
B)
C)
D)

Question 65

Evaluate the integral.

A)
B)
C)
D)

Question 66

Evaluate the integral.

A)
B)
C)
D)