Question 1

​Analytically determine the location of any horizontal asymptotes. ​   ​
​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no horizontal asymptotes 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no horizontal asymptotes

Question 2

​Find the derivative of the function

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 3

Find the slope of the tangent line to the graph of the function below at the given point. ​   ,   ​

Accepted Answer

A)  ​4 
B)  ​-4 
C)  ​-2 
D)  ​6 
E)  ​none of the above 
A)  ​4 
B)  ​-4 
C)  ​-2 
D)  ​6 
E)  ​none of the above

Question 4

Find the slope of the line passing through the pair of points. ​   and   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of the above 
A)    
B)    
C)    
D)    
E)  None of the above

Question 5

​Find the derivative of the function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 6

​Find the value   for the function   ​

Accepted Answer

A)  ​1,776 
B)  ​800 
C)  ​311 
D)  ​807 
E)  ​4,576 
A)  ​1,776 
B)  ​800 
C)  ​311 
D)  ​807 
E)  ​4,576

Question 7

​Write the equation of the line that passes through the given point and has the slope indicated.   with slope   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 8

​After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth   of its value for the previous year.Find a model for V(t),the value of the car after t years.

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 9

​A function and its graph are given.Use the second derivative to locate all x-values of points of inflection on the graph of   Check these results against the graph shown. ​
​   ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   ,   
E)  ​   ,   ,   
A)  ​   
B)  ​   
C)  ​   
D)  ​   ,   
E)  ​   ,   ,

Question 10

​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by   ,   ,where x is the number of machines used.How many machines give minimum average costs? ​

Accepted Answer

A)  ​Using 14 machines gives the minimum average costs. 
B)  ​Using zero machines gives the minimum average costs. 
C)  ​Using 24 machines gives the minimum average costs. 
D)  ​Using 28 machines gives the minimum average costs. 
E)  ​Using 33 machines gives the minimum average costs. 
A)  ​Using 14 machines gives the minimum average costs. 
B)  ​Using zero machines gives the minimum average costs. 
C)  ​Using 24 machines gives the minimum average costs. 
D)  ​Using 28 machines gives the minimum average costs. 
E)  ​Using 33 machines gives the minimum average costs.

Question 11

Find the slope of the tangent line to the graph of the function below at the given point. ​   ,   ​

Accepted Answer

A)  ​12 
B)  ​-3 
C)  ​-8 
D)  ​-12 
E)  ​none of the above 
A)  ​12 
B)  ​-3 
C)  ​-8 
D)  ​-12 
E)  ​none of the above

Question 12

Copy the points (-5,5),(3,-3),(-1,-2),(3,0),(1,-6)in the Cartesian plane. ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 13

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​
​   ,   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​both B and D 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​both B and D

Question 14

​The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long? ​

Accepted Answer

A)  ​96 ft2/min 
B)  1,008 ​ft2/min 
C)  504 ​ft2/min 
D)  ​2,016 ft2/min 
E)  ​84 ft2/min 
A)  ​96 ft2/min 
B)  1,008 ​ft2/min 
C)  504 ​ft2/min 
D)  ​2,016 ft2/min 
E)  ​84 ft2/min

Question 15

​Which of the following is the correct graph of   ? ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 16

Graph the function with a graphing utility and use it to predict the limit.Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​   ​

Accepted Answer

A)  ​   
B)  ​27 
C)  ​   
D)  ​0 
E)  ​does not exist 
A)  ​   
B)  ​27 
C)  ​   
D)  ​0 
E)  ​does not exist

Question 17

​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by   ,   ,where x is the number of machines used.What is the minimum average cost? ​

Accepted Answer

A)  ​$0 
B)  ​$35 
C)  ​$490 
D)  ​$245 
E)  ​$8582 
A)  ​$0 
B)  ​$35 
C)  ​$490 
D)  ​$245 
E)  ​$8582

Question 18

​Find   ​

Accepted Answer

A)  ​1 
B)  ​∞ 
C)  ​0 
D)  ​-1 
E)  ​-∞ 
A)  ​1 
B)  ​∞ 
C)  ​0 
D)  ​-1 
E)  ​-∞

Question 19

​Write the expression   as the logarithm of a single quantity.

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 20

​Find the derivative of the function

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Analytically determine the location of any horizontal asymptotes.

Find the derivative of the function

Find the slope of the tangent line to the graph of the function below at the given point. ,

Find the slope of the line passing through the pair of points. and

Find the derivative of the function.

Find the value for the function

Write the equation of the line that passes through the given point and has the slope indicated. with slope

After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth of its value for the previous year.Find a model for V(t),the value of the car after t years.

A function and its graph are given.Use the second derivative to locate all x-values of points of inflection on the graph of Check these results against the graph shown.

Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.How many machines give minimum average costs?

Find the slope of the tangent line to the graph of the function below at the given point. ,

Copy the points (-5,5),(3,-3),(-1,-2),(3,0),(1,-6)in the Cartesian plane.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?

Which of the following is the correct graph of ?

Graph the function with a graphing utility and use it to predict the limit.Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.

Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.What is the minimum average cost?

Find

Write the expression as the logarithm of a single quantity.

Find the derivative of the function

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 1: Functions, graphs, and Limits

​Analytically determine the location of any horizontal asymptotes. ​ ​ ​

​Find the derivative of the function

Find the slope of the tangent line to the graph of the function below at the given point. ​ , ​

Find the slope of the line passing through the pair of points. ​ and ​

​Find the derivative of the function. ​ ​ ​

​Find the value for the function ​

​Write the equation of the line that passes through the given point and has the slope indicated. with slope ​

​After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth of its value for the previous year.Find a model for V(t),the value of the car after t years.

​A function and its graph are given.Use the second derivative to locate all x-values of points of inflection on the graph of Check these results against the graph shown. ​ ​ ​ ​

​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.How many machines give minimum average costs? ​

Find the slope of the tangent line to the graph of the function below at the given point. ​ , ​

Copy the points (-5,5),(3,-3),(-1,-2),(3,0),(1,-6)in the Cartesian plane. ​

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ ​ , ​

​The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long? ​

​Which of the following is the correct graph of ? ​

Graph the function with a graphing utility and use it to predict the limit.Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​ ​

​Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.What is the minimum average cost? ​

​Find ​

​Write the expression as the logarithm of a single quantity.

​Find the derivative of the function

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Analytically determine the location of any horizontal asymptotes.

Find the derivative of the function

Find the slope of the tangent line to the graph of the function below at the given point. ,

Find the slope of the line passing through the pair of points. and

Find the derivative of the function.

Find the value for the function

Write the equation of the line that passes through the given point and has the slope indicated. with slope

After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth of its value for the previous year.Find a model for V(t),the value of the car after t years.

A function and its graph are given.Use the second derivative to locate all x-values of points of inflection on the graph of Check these results against the graph shown.

Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.How many machines give minimum average costs?

Find the slope of the tangent line to the graph of the function below at the given point. ,

Copy the points (-5,5),(3,-3),(-1,-2),(3,0),(1,-6)in the Cartesian plane.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?

Which of the following is the correct graph of ?

Graph the function with a graphing utility and use it to predict the limit.Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.

Average costs.Suppose the average costs of a mining operation depend on the number of machines used,and average costs,in dollars,are given by , ,where x is the number of machines used.What is the minimum average cost?

Find

Write the expression as the logarithm of a single quantity.

Find the derivative of the function