Question 1

Evaluate the expression   ​

Accepted Answer

A)  ​125 
B)  ​5 
C)  ​25 
D)  ​27 
E)  ​29 
A)  ​125 
B)  ​5 
C)  ​25 
D)  ​27 
E)  ​29

Question 2

​Given   and   ,find   ​

Accepted Answer

A)  ​3 
B)  ​17 
C)  ​6 
D)  ​-40 
E)  ​14 
A)  ​3 
B)  ​17 
C)  ​6 
D)  ​-40 
E)  ​14

Question 3

​An employee of a delivery company earns $25.00 per hour driving a delivery van in an area where gasoline costs $2.60 per gallon.When the van is driven at a constant speed s (in miles per hour,with   ),the van gets   miles per gallon.Determine the most economical speed s for a 100-mile trip on an interstate highway. ​

Accepted Answer

A)  ​The most economical speed is 52.0 mph. 
B)  ​The most economical speed is 48.0 mph. 
C)  ​The most economical speed is 25.0 mph. 
D)  ​The most economical speed is 50.0 mph. 
E)  ​The most economical speed is 53.0 mph. 
A)  ​The most economical speed is 52.0 mph. 
B)  ​The most economical speed is 48.0 mph. 
C)  ​The most economical speed is 25.0 mph. 
D)  ​The most economical speed is 50.0 mph. 
E)  ​The most economical speed is 53.0 mph.

Question 4

​Write the equation of the line passing through the given pair of points.       ​

Accepted Answer

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

Question 5

Determine whether y is a function of x. ​
​   ​

Accepted Answer

A)  ​Yes 
B)  ​No 
A)  ​Yes 
B)  ​No

Question 6

​Find the second derivative of the function   ​

Accepted Answer

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

Question 7

​Solve   for t.Round your answer to four decimal places. ​

Accepted Answer

A)  ​1.4454 
B)  ​0.3611 
C)  ​2.6344 
D)  ​0.3614 
E)  ​2.7184 
A)  ​1.4454 
B)  ​0.3611 
C)  ​2.6344 
D)  ​0.3614 
E)  ​2.7184

Question 8

​Sketch the graph of the function   using any extrema,intercepts,symmetry,and asymptotes. ​

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

​Describe the interval(s)on which the function   is continuous. ​

Accepted Answer

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

Question 11

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is   Find the rate of change of A with respect to r when   Round your answer to two decimal places. ​

Accepted Answer

A)  $1,375.67 
B)  $65,594.67 
C)  $114.64 
D)  $5,466.22 
E)  $5,430.02 
A)  $1,375.67 
B)  $65,594.67 
C)  $114.64 
D)  $5,466.22 
E)  $5,430.02

Question 12

​This problem contains a function and its graph,where   Use the graph to determine,as well as you can,the horizontal asymptote.Check your conclusion by using the function to determine the horizontal asymptote analytically. ​
​   ​
​   ​

Accepted Answer

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

Question 13

​Find the second derivative for the function   and solve the equation   ​

Accepted Answer

A)  ​-2 
B)  ​1 
C)  ​0 
D)  ​26 
E)  ​33 
A)  ​-2 
B)  ​1 
C)  ​0 
D)  ​26 
E)  ​33

Question 14

​For the function given,find   ​ ​   ​

Accepted Answer

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

Question 15

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

Accepted Answer

A)  ​-12 
B)  ​   
C)  ​2 
D)  ​   
E)  ​The slope is undefined. 
A)  ​-12 
B)  ​   
C)  ​2 
D)  ​   
E)  ​The slope is undefined.

Question 16

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 17

Determine whether the given function is continuous.If it is not,identify where it is discontinuous and which condition fails to hold.You can verify your conclusions by graphing the function with a graphing utility,if one is available. ​   ​​

Accepted Answer

A)  ​discontinuous at   
B)  ​​discontinuous at   
C)  ​​discontinuous at   
D)  ​​discontinuous at   
E)  ​continuous everywhere 
A)  ​discontinuous at   
B)  ​​discontinuous at   
C)  ​​discontinuous at   
D)  ​​discontinuous at   
E)  ​continuous everywhere

Question 18

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 19

​Find the derivative of the function   ​

Accepted Answer

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

Question 20

Identify the open intervals where the function   is increasing or decreasing. ​

Accepted Answer

A)  ​decreasing:   ; increasing:   
B)  ​​increasing:   ; decreasing:   
C)  ​increasing on   
D)  ​​decreasing on   
E)  ​none of the above 
A)  ​decreasing:   ; increasing:   
B)  ​​increasing:   ; decreasing:   
C)  ​increasing on   
D)  ​​decreasing on   
E)  ​none of the above

Evaluate the expression

Given and ,find

Write the equation of the line passing through the given pair of points.

Determine whether y is a function of x.

Find the second derivative of the function

Solve for t.Round your answer to four decimal places.

Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes.

Solve the following equation for accurate to three decimal places.

Describe the interval(s)on which the function is continuous.

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places.

This problem contains a function and its graph,where Use the graph to determine,as well as you can,the horizontal asymptote.Check your conclusion by using the function to determine the horizontal asymptote analytically.

Find the second derivative for the function and solve the equation

For the function given,find

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

Find the derivative of the following function.

Determine whether the given function is continuous.If it is not,identify where it is discontinuous and which condition fails to hold.You can verify your conclusions by graphing the function with a graphing utility,if one is available.

Find the derivative of the following function.

Find the derivative of the function

Identify the open intervals where the function is increasing or decreasing.

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

Evaluate the expression ​

​Given and ,find ​

​Write the equation of the line passing through the given pair of points. ​

Determine whether y is a function of x. ​ ​ ​

​Find the second derivative of the function ​

​Solve for t.Round your answer to four decimal places. ​

​Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. ​

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

​Describe the interval(s)on which the function is continuous. ​

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places. ​

​This problem contains a function and its graph,where Use the graph to determine,as well as you can,the horizontal asymptote.Check your conclusion by using the function to determine the horizontal asymptote analytically. ​ ​ ​ ​ ​

​Find the second derivative for the function and solve the equation ​

​For the function given,find ​ ​ ​

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

​Find the derivative of the following function. ​ ​

Determine whether the given function is continuous.If it is not,identify where it is discontinuous and which condition fails to hold.You can verify your conclusions by graphing the function with a graphing utility,if one is available. ​ ​​

​Find the derivative of the following function. ​ ​

​Find the derivative of the function ​

Identify the open intervals where the function is increasing or decreasing. ​

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

Evaluate the expression

Given and ,find

Write the equation of the line passing through the given pair of points.

Determine whether y is a function of x.

Find the second derivative of the function

Solve for t.Round your answer to four decimal places.

Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes.

Solve the following equation for accurate to three decimal places.

Describe the interval(s)on which the function is continuous.

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places.

This problem contains a function and its graph,where Use the graph to determine,as well as you can,the horizontal asymptote.Check your conclusion by using the function to determine the horizontal asymptote analytically.

Find the second derivative for the function and solve the equation

For the function given,find

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

Find the derivative of the following function.

Determine whether the given function is continuous.If it is not,identify where it is discontinuous and which condition fails to hold.You can verify your conclusions by graphing the function with a graphing utility,if one is available.

Find the derivative of the following function.

Find the derivative of the function

Identify the open intervals where the function is increasing or decreasing.