Question 1

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

Accepted Answer

A)  continuous everywhere 
B)    , removable 
C)    , removable 
D)    , removable 
E)  both B and C 
A)  continuous everywhere 
B)    , removable 
C)    , removable 
D)    , removable 
E)  both B and C

Question 2

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

Accepted Answer

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

Question 3

​Simplify   ​

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

A)  ​   
B)  ​1 
C)  ​-11 
D)  ​5 
E)  ​The slope is undefined. 
A)  ​   
B)  ​1 
C)  ​-11 
D)  ​5 
E)  ​The slope is undefined.

Question 6

​Use a table utility with x-values larger than 10,000 to investigate   What does the table indicate about   ?   ​

Accepted Answer

A)  ​- 2 
B)  ​2 
C)  ​4 
D)  ​0 
E)  ​does not exist 
A)  ​- 2 
B)  ​2 
C)  ​4 
D)  ​0 
E)  ​does not exist

Question 7

​Find the extrema of the function   ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

​Find   ,if

Accepted Answer

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

Question 10

​The population P ( in thousands)of Japan from 1980 through 2010 can be modeled by   where t is the year,with   corresponding to 1980.Determine the population growth rate,   ​

Accepted Answer

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

Question 11

​Find the derivative of the function. ​
​   ​

Accepted Answer

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

Question 12

​A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used. ​

Accepted Answer

A)  ​14, 14 
B)  ​12, 12 
C)  ​10, 10 
D)  ​13, 13 
E)  ​11,11 
A)  ​14, 14 
B)  ​12, 12 
C)  ​10, 10 
D)  ​13, 13 
E)  ​11,11

Question 13

​The inventor of a new game believes that the variable cost for producing the game is $0.98 per unit.The fixed cost is $7000. Find a formula for the average cost per unit   ​

Accepted Answer

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

Question 14

​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 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

Accepted Answer

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

Question 15

​Compare dy and Δy for   at ​x​ = 1 with Δ​x​ = dx = -0.09.Give your answers to four decimal places. ​

Accepted Answer

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

Question 16

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. ​   ​

Accepted Answer

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

Question 17

​Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.
​

Accepted Answer

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

Question 18

​Locate any relative extrema and inflection points of the function   ​

Accepted Answer

A)  ​no relative extrema; inflection point at   
B)  ​relative maximum at   ; inflection point at   
C)  ​relative minimum at   ; inflection point at   
D)  ​no relative extrema; inflection point at   
E)  ​relative minimum at   ; no inflection points 
A)  ​no relative extrema; inflection point at   
B)  ​relative maximum at   ; inflection point at   
C)  ​relative minimum at   ; inflection point at   
D)  ​no relative extrema; inflection point at   
E)  ​relative minimum at   ; no inflection points

Question 19

​Use a graphing utility to graph the function   Be sure to choose an appropriate viewing window. ​

Accepted Answer

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

Question 20

​If   find   ​

Accepted Answer

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

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

Estimate the slope of the line from the graph.

Simplify

Write the equation of the line through that is parallel to

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

Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ?

Find the extrema of the function

Write the expression as the logarithm of a single quantity.

Find ,if

The population P ( in thousands)of Japan from 1980 through 2010 can be modeled by where t is the year,with corresponding to 1980.Determine the population growth rate,

Find the derivative of the function.

A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used.

The inventor of a new game believes that the variable cost for producing the game is $0.98 per unit.The fixed cost is $7000. Find a formula for the average cost per unit

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 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

Compare dy and Δy for at x = 1 with Δx = dx = -0.09.Give your answers to four decimal places.

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms.

Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.

Locate any relative extrema and inflection points of the function

Use a graphing utility to graph the function Be sure to choose an appropriate viewing window.

If find

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

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

​Simplify ​

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

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

​Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ? ​

​Find the extrema of the function ​

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

​Find ,if

​The population P ( in thousands)of Japan from 1980 through 2010 can be modeled by where t is the year,with corresponding to 1980.Determine the population growth rate, ​

​Find the derivative of the function. ​ ​ ​

​A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used. ​

​The inventor of a new game believes that the variable cost for producing the game is $0.98 per unit.The fixed cost is $7000. Find a formula for the average cost per unit ​

​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 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

​Compare dy and Δy for at ​x​ = 1 with Δ​x​ = dx = -0.09.Give your answers to four decimal places. ​

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. ​ ​

​Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6. ​

​Locate any relative extrema and inflection points of the function ​

​Use a graphing utility to graph the function Be sure to choose an appropriate viewing window. ​

​If find ​

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

Estimate the slope of the line from the graph.

Simplify

Write the equation of the line through that is parallel to

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

Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ?

Find the extrema of the function

Write the expression as the logarithm of a single quantity.

Find ,if

The population P ( in thousands)of Japan from 1980 through 2010 can be modeled by where t is the year,with corresponding to 1980.Determine the population growth rate,

Find the derivative of the function.

A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used.

The inventor of a new game believes that the variable cost for producing the game is $0.98 per unit.The fixed cost is $7000. Find a formula for the average cost per unit

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 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

Compare dy and Δy for at x = 1 with Δx = dx = -0.09.Give your answers to four decimal places.

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms.

Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.

Locate any relative extrema and inflection points of the function

Use a graphing utility to graph the function Be sure to choose an appropriate viewing window.

If find