Question 1

​Use the properties of logarithms to write the expression as a single logarithm. ​   ​

Accepted Answer

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

Question 2

When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​

Accepted Answer

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

Question 3

Sketch the graph of the function   ? ​

Accepted Answer

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

Question 4

​Write the equation of the line through   that is perpendicular to   ​

Accepted Answer

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

Question 5

Use a graphing utility to graph the function   ​ ​

Accepted Answer

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

Question 6

​Find the third derivative of the function   ​

Accepted Answer

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

Question 7

​If the total revenue function for a blender is   ,determine how many units x must be sold to provide the maximum total revenue in dollars. ​

Accepted Answer

A)  ​625 
B)  ​15,000 
C)  ​25 
D)  ​300 
E)  ​50 
A)  ​625 
B)  ​15,000 
C)  ​25 
D)  ​300 
E)  ​50

Question 8

​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where   Confirm your results analytically.​ ​
​   ​
​

Accepted Answer

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

Question 9

​Analyze and sketch a graph of the function   ​

Accepted Answer

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

Question 10

​Suppose that   and   Find the following limit: ​   ​

Accepted Answer

A)  ​13 
B)  ​24 
C)  ​2 
D)  ​-143 
E)  ​11 
A)  ​13 
B)  ​24 
C)  ​2 
D)  ​-143 
E)  ​11

Question 11

​Find   ,if   ​

Accepted Answer

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

Question 12

Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of     ​

Accepted Answer

A)  length 1.5; width 1.25 
B)  length 2; width 1 
C)  length 0.5; width 1.75 
D)  length 1; width 1.5 
E)  none of the above 
A)  length 1.5; width 1.25 
B)  length 2; width 1 
C)  length 0.5; width 1.75 
D)  length 1; width 1.5 
E)  none of the above

Question 13

​Find the x-values (if any)at which the function   is not continuous.Which of the discontinuities are removable? ​

Accepted Answer

A)  ​no points of discontinuity 
B)  ​   (not removable),   (removable) 
C)  ​   (removable),   (not removable) 
D)  no points of continuity 
E)  ​​   (not removable),   (not removable) 
A)  ​no points of discontinuity 
B)  ​   (not removable),   (removable) 
C)  ​   (removable),   (not removable) 
D)  no points of continuity 
E)  ​​   (not removable),   (not removable)

Question 14

​Find all relative minima of the given function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no relative maxima 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no relative maxima

Question 15

​For the given function,find the relative minima. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no relative minima 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no relative minima

Question 16

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as   Find the derivative of the model. ​

Accepted Answer

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

Question 17

Find   for the equation   by implicit differentiation and evaluate the derivative at the point   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  0 
A)    
B)    
C)    
D)    
E)  0

Question 18

What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.

Accepted Answer

A)  $147,330.10 
B)  $18,292.68 
C)  $53,571.43 
D)  $24,961.93 
E)  $25,294.49 
A)  $147,330.10 
B)  $18,292.68 
C)  $53,571.43 
D)  $24,961.93 
E)  $25,294.49

Question 19

​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 20

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Use the properties of logarithms to write the expression as a single logarithm.

Sketch the graph of the function ?

Write the equation of the line through that is perpendicular to

Use a graphing utility to graph the function

Find the third derivative of the function

If the total revenue function for a blender is ,determine how many units x must be sold to provide the maximum total revenue in dollars.

A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.

Analyze and sketch a graph of the function

Suppose that and Find the following limit:

Find ,if

Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of

Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable?

Find all relative minima of the given function.

For the given function,find the relative minima.

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model.

Find for the equation by implicit differentiation and evaluate the derivative at the point

What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.

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

Find the derivative of the following 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

​Use the properties of logarithms to write the expression as a single logarithm. ​ ​

Sketch the graph of the function ? ​

​Write the equation of the line through that is perpendicular to ​

Use a graphing utility to graph the function ​ ​

​Find the third derivative of the function ​

​If the total revenue function for a blender is ,determine how many units x must be sold to provide the maximum total revenue in dollars. ​

​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​

​Analyze and sketch a graph of the function ​

​Suppose that and Find the following limit: ​ ​

​Find ,if ​

Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of ​

​Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable? ​

​Find all relative minima of the given function. ​ ​ ​

​For the given function,find the relative minima. ​ ​ ​

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​

Find for the equation by implicit differentiation and evaluate the derivative at the point ​

What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.

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

​Find the derivative of the following 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

Use the properties of logarithms to write the expression as a single logarithm.

Sketch the graph of the function ?

Write the equation of the line through that is perpendicular to

Use a graphing utility to graph the function

Find the third derivative of the function

If the total revenue function for a blender is ,determine how many units x must be sold to provide the maximum total revenue in dollars.

A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.

Analyze and sketch a graph of the function

Suppose that and Find the following limit:

Find ,if

Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of

Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable?

Find all relative minima of the given function.

For the given function,find the relative minima.

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model.

Find for the equation by implicit differentiation and evaluate the derivative at the point

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

Find the derivative of the following function.