Question 1

​Find   ,if   ​

Accepted Answer

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

Question 2

​With an annual rate of inflation of 4% over the next 10 years,the approximate cost of goods or services during any year in the decade is given by   where t is the time (in years)and P is the present cost.The price of an oil change for a car is presently $24.95.Estimate the price 10 years from now.Round your answer to the nearest cent.

Accepted Answer

A)  ​​$37.09 
B)  ​$36.93 
C)  ​​$89.00 
D)  ​​$63.90 
A)  ​​$37.09 
B)  ​$36.93 
C)  ​​$89.00 
D)  ​​$63.90

Question 3

​If the total revenue function for a blender is   ,find the maximum revenue. ​

Accepted Answer

A)  ​$100 
B)  ​$2,500 
C)  ​$40 
D)  ​$250 
E)  ​$2,000 
A)  ​$100 
B)  ​$2,500 
C)  ​$40 
D)  ​$250 
E)  ​$2,000

Question 4

Differentiate the given function. ​   ​

Accepted Answer

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

Question 5

​Find any vertical asymptotes for the given function. ​
​   ​

Accepted Answer

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

Question 6

​Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.3/min.At what rate is the radius of the balloon increasing when the radius is 7 in.? ​

Accepted Answer

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

Question 7

​Suppose that   and   Find the following limit: ​   ​

Accepted Answer

A)  ​7 
B)  ​6 
C)  ​0 
D)  ​8 
E)  ​1 
A)  ​7 
B)  ​6 
C)  ​0 
D)  ​8 
E)  ​1

Question 8

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

Accepted Answer

A)  ​$9,800 
B)  ​​$9,850 
C)  ​​$8,800 
D)  ​​$8,850 
E)  ​​​$9,750 
A)  ​$9,800 
B)  ​​$9,850 
C)  ​​$8,800 
D)  ​​$8,850 
E)  ​​​$9,750

Question 9

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

Accepted Answer

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

Question 10

​Use the product Rule to find the derivative of the function   ​

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

​Suppose the sales S (in billions of dollars per year)for Proctor & Gamble for the years 1997 through 2002 can be modeled by   ,   where t represents the year.During which year were the sales increasing at the lowest rate? ​

Accepted Answer

A)  ​Sales are increasing at the lowest rate in the year 2002. 
B)  ​Sales are increasing at the lowest rate in the year 1997. 
C)  ​Sales are increasing at the lowest rate in the year 1998. 
D)  ​Sales are increasing at the lowest rate in the year 2000. 
E)  ​Sales are increasing at the lowest rate in the year 1999. 
A)  ​Sales are increasing at the lowest rate in the year 2002. 
B)  ​Sales are increasing at the lowest rate in the year 1997. 
C)  ​Sales are increasing at the lowest rate in the year 1998. 
D)  ​Sales are increasing at the lowest rate in the year 2000. 
E)  ​Sales are increasing at the lowest rate in the year 1999.

Question 13

​Use implicit differentiation to find   ​   ​

Accepted Answer

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

Question 14

​A travel agency will plan a tour for groups of size 53 or larger.If the group contains exactly 53 people,the price is $800 per person.However,each person's price is reduced by $10 for each additional person above the 53.If the travel agency incurs a price of $150 per person for the tour,what size group will give the agency the maximum profit?

Accepted Answer

A)  ​6 
B)  ​91 
C)  ​59 
D)  ​70 
E)  ​32 
A)  ​6 
B)  ​91 
C)  ​59 
D)  ​70 
E)  ​32

Question 15

The cost (in dollars)of removing p% of the pollutants from the water in a small lake is given by   ,   Evaluate   ​

Accepted Answer

A)  ​∞ 
B)  ​23,000 
C)  ​0 
D)  ​-23000 
E)  ​-∞ 
A)  ​∞ 
B)  ​23,000 
C)  ​0 
D)  ​-23000 
E)  ​-∞

Question 16

​Sketch the graph of the function   ​

Accepted Answer

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

Question 17

Sketch the graph of the equation:   ​

Accepted Answer

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

Question 18

Use the Horizontal Line Test to determine whether the functions are one-to-one. ​     ​ ​

Accepted Answer

A)  ​f(x) and g(x) both are one-to-one. 
B)  ​f(x) is not one-to-one and g(x) is one-to-one. 
C)  ​f(x) and g(x) both are not one-to-one. 
D)  ​f(x) is one-to-one and g(x) is not one-to-one. 
A)  ​f(x) and g(x) both are one-to-one. 
B)  ​f(x) is not one-to-one and g(x) is one-to-one. 
C)  ​f(x) and g(x) both are not one-to-one. 
D)  ​f(x) is one-to-one and g(x) is not one-to-one.

Question 19

​Find the   of   ​

Accepted Answer

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

Question 20

​Find   ,   ,and   of the functions   ,   ​

Accepted Answer

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

Find ,if

If the total revenue function for a blender is ,find the maximum revenue.

Differentiate the given function.

Find any vertical asymptotes for the given function.

Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.³/min.At what rate is the radius of the balloon increasing when the radius is 7 in.?

Suppose that and Find the following limit:

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

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

Use the product Rule to find the derivative of the function

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

Suppose the sales S (in billions of dollars per year)for Proctor & Gamble for the years 1997 through 2002 can be modeled by , where t represents the year.During which year were the sales increasing at the lowest rate?

Use implicit differentiation to find

The cost (in dollars)of removing p% of the pollutants from the water in a small lake is given by , Evaluate

Sketch the graph of the function

Sketch the graph of the equation:

Use the Horizontal Line Test to determine whether the functions are one-to-one.

Find the of

Find , ,and of the functions ,

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 ,if ​

​If the total revenue function for a blender is ,find the maximum revenue. ​

Differentiate the given function. ​ ​

​Find any vertical asymptotes for the given function. ​ ​ ​

​Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.3/min.At what rate is the radius of the balloon increasing when the radius is 7 in.? ​

​Suppose that and Find the following limit: ​ ​

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

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

​Use the product Rule to find the derivative of the function ​

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

​Suppose the sales S (in billions of dollars per year)for Proctor & Gamble for the years 1997 through 2002 can be modeled by , where t represents the year.During which year were the sales increasing at the lowest rate? ​

​Use implicit differentiation to find ​ ​

The cost (in dollars)of removing p% of the pollutants from the water in a small lake is given by , Evaluate ​

​Sketch the graph of the function ​

Sketch the graph of the equation: ​

Use the Horizontal Line Test to determine whether the functions are one-to-one. ​ ​ ​

​Find the of ​

​Find , ,and of the functions , ​

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 ,if

If the total revenue function for a blender is ,find the maximum revenue.

Differentiate the given function.

Find any vertical asymptotes for the given function.

Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.³/min.At what rate is the radius of the balloon increasing when the radius is 7 in.?

Suppose that and Find the following limit:

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

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

Use the product Rule to find the derivative of the function

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

Suppose the sales S (in billions of dollars per year)for Proctor & Gamble for the years 1997 through 2002 can be modeled by , where t represents the year.During which year were the sales increasing at the lowest rate?

Use implicit differentiation to find

The cost (in dollars)of removing p% of the pollutants from the water in a small lake is given by , Evaluate

Sketch the graph of the function

Sketch the graph of the equation:

Use the Horizontal Line Test to determine whether the functions are one-to-one.

Find the of

Find , ,and of the functions ,