Question 1

Find   ​   ​

Accepted Answer

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

Question 2

​Analyze and sketch a graph of the function   ​

Accepted Answer

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

Question 3

Find the derivative of the function. ​
​   ​

Accepted Answer

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

Question 4

Solve the following equation for x accurate to three decimal places. ​   ​

Accepted Answer

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

Question 5

​Sketch the graph of the function   and describe the interval(s)on which the function is continuous. ​

Accepted Answer

A)  ​​   and     
B)  ​   and     
C)  ​   and     
D)  ​   and  
​   
E)  ​none of these choices 
A)  ​​   and     
B)  ​   and     
C)  ​   and     
D)  ​   and  
​   
E)  ​none of these choices

Question 6

Use the graph of   to identify at which of the indicated points the derivative   changes from negative to positive. ​   ​
​

Accepted Answer

A)  (2,4), (5,6) 
B)  (-1,2) 
C)  (-1,2), (2,4) 
D)  (2,4) 
E)  (-1,2),(5,6) 
A)  (2,4), (5,6) 
B)  (-1,2) 
C)  (-1,2), (2,4) 
D)  (2,4) 
E)  (-1,2),(5,6)

Question 7

​Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years   ,   Round your answer to the nearest cent. ​

Accepted Answer

A)  ​$49787.07 
B)  ​$50787.07 
C)  ​$49000.04 
D)  ​$40000.06 
A)  ​$49787.07 
B)  ​$50787.07 
C)  ​$49000.04 
D)  ​$40000.06

Question 8

​If   ,find

Accepted Answer

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

Question 9

The cost of producing x units of a product is modeled by   Find the average cost function   ​

Accepted Answer

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

Question 10

​Find the open intervals on which the function   is increasing or decreasing. ​

Accepted Answer

A)  ​The function is increasing on the interval   and decreasing on the interval   
B)  ​The function is increasing on the interval   and decreasing on the interval   
C)  ​The function is increasing on the interval   and decreasing on the interval   
D)  ​The function is increasing on the interval   and decreasing on the interval   
E)  ​The function is increasing on the interval   and decreasing on the interval   
A)  ​The function is increasing on the interval   and decreasing on the interval   
B)  ​The function is increasing on the interval   and decreasing on the interval   
C)  ​The function is increasing on the interval   and decreasing on the interval   
D)  ​The function is increasing on the interval   and decreasing on the interval   
E)  ​The function is increasing on the interval   and decreasing on the interval

Question 11

​Use a calculator to evaluate the logarithm   Round your answer to three decimal places.

Accepted Answer

A)  ​0.195 
B)  ​2.464 
C)  ​6.402 
D)  ​3.737 
E)  ​5.129 
A)  ​0.195 
B)  ​2.464 
C)  ​6.402 
D)  ​3.737 
E)  ​5.129

Question 12

​Find​     ​

Accepted Answer

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

Question 13

​Find   ,if   ​

Accepted Answer

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

Question 14

​Find the marginal revenue for producing x units.(The revenue is measured in dollars.) ​   ​

Accepted Answer

A)  ​   dollars 
B)  ​​   dollars 
C)  ​​50 dollars 
D)  ​​   dollars 
E)  ​​​   dollars 
A)  ​   dollars 
B)  ​​   dollars 
C)  ​​50 dollars 
D)  ​​   dollars 
E)  ​​​   dollars

Question 15

​Determine the range of the function   ​ ​   ​

Accepted Answer

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

Question 16

​A fast-food restaurant determines the cost model,   and revenue model,   for   where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing. ​
​

Accepted Answer

A)  ​The profit function is increasing on the interval   and decreasing on the interval   
B)  ​The profit function is increasing on the interval   and decreasing on the interval   
C)  ​​The profit function is increasing on the interval   and decreasing on the interval   
D)  ​The profit function is increasing on the interval   and decreasing on the interval   
E)  ​​The profit function is increasing on the interval   and decreasing on the interval   
A)  ​The profit function is increasing on the interval   and decreasing on the interval   
B)  ​The profit function is increasing on the interval   and decreasing on the interval   
C)  ​​The profit function is increasing on the interval   and decreasing on the interval   
D)  ​The profit function is increasing on the interval   and decreasing on the interval   
E)  ​​The profit function is increasing on the interval   and decreasing on the interval

Question 17

​Find   implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating   at the point. ​   ​   ​

Accepted Answer

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

Question 18

​Estimate the slope of the line from the graph. ​   ​
​

Accepted Answer

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

Question 19

Find the midpoint of the line segment joining between the points (7,-1)and (2,-6).Round your answer to the nearest hundredth if necessary. ​

Accepted Answer

A)  (4, 2.5) 
B)  (4.5, -3.5) 
C)  (14, 6) 
D)  (3, -2) 
E)  none of these choices 
A)  (4, 2.5) 
B)  (4.5, -3.5) 
C)  (14, 6) 
D)  (3, -2) 
E)  none of these choices

Question 20

​The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle. ​

Accepted Answer

A)  ​3.70 % 
B)  ​1.30 % 
C)  ​2.59 % 
D)  ​5.19 % 
E)  ​1.85 % 
A)  ​3.70 % 
B)  ​1.30 % 
C)  ​2.59 % 
D)  ​5.19 % 
E)  ​1.85 %

Find

Analyze and sketch a graph of the function

Find the derivative of the function.

Solve the following equation for x accurate to three decimal places.

Sketch the graph of the function and describe the interval(s)on which the function is continuous.

Use the graph of to identify at which of the indicated points the derivative changes from negative to positive.

Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years , Round your answer to the nearest cent.

If ,find

The cost of producing x units of a product is modeled by Find the average cost function

Find the open intervals on which the function is increasing or decreasing.

Use a calculator to evaluate the logarithm Round your answer to three decimal places.

Find

Find ,if

Find the marginal revenue for producing x units.(The revenue is measured in dollars.)

Determine the range of the function

A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing.

Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point.

Estimate the slope of the line from the graph.

Find the midpoint of the line segment joining between the points (7,-1)and (2,-6).Round your answer to the nearest hundredth if necessary.

The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle.

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

Find ​ ​

​Analyze and sketch a graph of the function ​

Find the derivative of the function. ​ ​ ​

Solve the following equation for x accurate to three decimal places. ​ ​

​Sketch the graph of the function and describe the interval(s)on which the function is continuous. ​

Use the graph of to identify at which of the indicated points the derivative changes from negative to positive. ​ ​ ​

​Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years , Round your answer to the nearest cent. ​

​If ,find

The cost of producing x units of a product is modeled by Find the average cost function ​

​Find the open intervals on which the function is increasing or decreasing. ​

​Use a calculator to evaluate the logarithm Round your answer to three decimal places.

​Find​ ​

​Find ,if ​

​Find the marginal revenue for producing x units.(The revenue is measured in dollars.) ​ ​

​Determine the range of the function ​ ​ ​

​A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing. ​ ​

​Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point. ​ ​ ​

​Estimate the slope of the line from the graph. ​ ​ ​

Find the midpoint of the line segment joining between the points (7,-1)and (2,-6).Round your answer to the nearest hundredth if necessary. ​

​The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle. ​

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

Find

Analyze and sketch a graph of the function

Find the derivative of the function.

Solve the following equation for x accurate to three decimal places.

Sketch the graph of the function and describe the interval(s)on which the function is continuous.

Use the graph of to identify at which of the indicated points the derivative changes from negative to positive.

Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years , Round your answer to the nearest cent.

If ,find

The cost of producing x units of a product is modeled by Find the average cost function

Find the open intervals on which the function is increasing or decreasing.

Use a calculator to evaluate the logarithm Round your answer to three decimal places.

Find

Find ,if

Find the marginal revenue for producing x units.(The revenue is measured in dollars.)

Determine the range of the function

A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing.

Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point.

Estimate the slope of the line from the graph.

Find the midpoint of the line segment joining between the points (7,-1)and (2,-6).Round your answer to the nearest hundredth if necessary.

The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle.