Question 1

Graph the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)    C

Question 2

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)    B

Question 3

Use the given graph to sketch the inverse function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)    A

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

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.

Accepted Answer

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

Question 6

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

Accepted Answer

The answer of Show that   and  ...

Question 7

Evaluate the limit.

Accepted Answer

A)  1 
B)  0 
C)    
D)  indeterminant 
A)  1 
B)  0 
C)    
D)  indeterminant

Question 8

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

Accepted Answer

Answer details may vary. @#IMG-DLM& Addi

Question 9

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.

Accepted Answer

Answer details may vary.
Derivative of p

Question 10

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

Accepted Answer

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

Question 11

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).

Accepted Answer

A)      
B)      
C)      
D)      
A)      
B)      
C)      
D)

Question 12

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

Accepted Answer

The function is not

Question 13

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Evaluate the integral exactly.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

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.

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Find all solutions.

Accepted Answer

A)    or   
B)    or   
C)    
D)    or   
A)    or   
B)    or   
C)    
D)    or

Question 19

Find all extrema and inflection points.

Accepted Answer

A)  extrema at   inflection points at   
B)  no extrema inflection point at   
C)  extremum at   inflection points at   
D)  extremum at   inflection points at   
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 20

Use a triangle to simplify the expression.   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Graph the function.

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

Use the given graph to sketch the inverse function.

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

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.

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

Evaluate the limit.

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

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.

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

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

Evaluate the integral.

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

Evaluate the integral exactly.

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.

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

Find all solutions.

Find all extrema and inflection points.

Use a triangle to simplify the expression. .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 7: Exponentials, Logarithms and Other Transcendental Functions

Graph the function.

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

Use the given graph to sketch the inverse function.

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

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.

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

Evaluate the limit.

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

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.

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

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

Evaluate the integral.

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

Evaluate the integral exactly.

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.

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

Find all solutions.

Find all extrema and inflection points.

Use a triangle to simplify the expression. .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters