Question 1

​Use the graph f '' to sketch the graph of ​f​. ​   ​

Accepted Answer

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

Question 2

To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.

Accepted Answer

A)  $3,240.96 
B)  $3,260.41 
C)  $3,186.49 
D)  $2,926.00 
E)  $16,475.16 
A)  $3,240.96 
B)  $3,260.41 
C)  $3,186.49 
D)  $2,926.00 
E)  $16,475.16

Question 3

These three points are collinear. ​   ,   ,   ​

Accepted Answer

A) True 
 B)False

Question 4

​The profit (in dollars)from selling x units of calculus textbooks is given by   Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places. ​

Accepted Answer

A)  ​$15.35 
B)  ​$30.00 
C)  ​$15.45 
D)  ​$30.80 
E)  ​$30.60 
A)  ​$15.35 
B)  ​$30.00 
C)  ​$15.45 
D)  ​$30.80 
E)  ​$30.60

Question 5

​A brick becomes dislodged from the Empire State Building (at a height of 1,000 feet)and falls to the sidewalk below.Write the position s(t),velocity v(t),and acceleration a(t)as functions of time. ​

Accepted Answer

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

Question 6

​Assume that x and y are differentiable functions of t.Find   using the given values. ​   for   ,   ​

Accepted Answer

A)  ​216 
B)  ​82 
C)  ​164 
D)  ​214 
E)  ​107 
A)  ​216 
B)  ​82 
C)  ​164 
D)  ​214 
E)  ​107

Question 7

​Carbon-14 (14C)dating assumes that the carbon on the Earth today has the same radioactive content as it did centuries ago.If this is true,then the amount of 14C absorbed by a tree that grew several centuries ago should be the same as the amount of 14C absorbed by a similar tree today.A piece of ancient charcoal contains only 24% as much of the radioactive carbon as a piece of modern charcoal.How long ago was the tree burned to make the ancient charcoal? (The half-life of 14C is 5715 years.)Round your answer to the nearest integer. ​

Accepted Answer

A)  ​2,776 years 
B)  ​30,751 years 
C)  ​2,781 years 
D)  ​11,767 years 
E)  ​11,772 years 
A)  ​2,776 years 
B)  ​30,751 years 
C)  ​2,781 years 
D)  ​11,767 years 
E)  ​11,772 years

Question 8

The demand function for a product is modeled by   What is the limit of the price as x increases without bound?

Accepted Answer

A)  The limit of the price as x increases without bound is -1. 
B)  The limit of the price as x increases without bound is 1. 
C)  The limit of the price as x increases without bound is 0. 
D)  The limit of the price as x increases without bound is 3,000. 
E)  The limit of the price as x increases without bound is 4. 
A)  The limit of the price as x increases without bound is -1. 
B)  The limit of the price as x increases without bound is 1. 
C)  The limit of the price as x increases without bound is 0. 
D)  The limit of the price as x increases without bound is 3,000. 
E)  The limit of the price as x increases without bound is 4.

Question 9

​Find an equation of the tangent line to the graph of f at the given point. ​   ,at   ​

Accepted Answer

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

Question 10

​Solve the exponential equation.Give the answer correct to 3 decimal places. ​   ​

Accepted Answer

A)  ​0.675 
B)  ​3.374 
C)  ​7.410 
D)  ​0.599 
E)  ​14.979 
A)  ​0.675 
B)  ​3.374 
C)  ​7.410 
D)  ​0.599 
E)  ​14.979

Question 11

​Use the limit definition to find the slope of the tangent line to the graph of   at the point   ​

Accepted Answer

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

Question 12

​Which of the following is the correct graph of   ? ​

Accepted Answer

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

Question 13

​Sketch a graph of a function f having the following characteristics. ​
​           ​

Accepted Answer

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

Question 14

If   ,find   ​ ​

Accepted Answer

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

Question 15

​Solve for the equation for   ​

Accepted Answer

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

Question 16

​Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​does not exist 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​does not exist

Question 17

Use the point   on a line having slope   to find two additional points through which the line passes. ​

Accepted Answer

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

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 slope of the graph at the given point. ​   ​   ​

Accepted Answer

A)  ​2 
B)  ​0 
C)  ​1 
D)  ​3 
E)  ​5 
A)  ​2 
B)  ​0 
C)  ​1 
D)  ​3 
E)  ​5

Question 20

​Find the derivative of the following function using the limiting process. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​either B or D 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​either B or D

Use the graph f '' to sketch the graph of f.

To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.

These three points are collinear. , ,

The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places.

A brick becomes dislodged from the Empire State Building (at a height of 1,000 feet)and falls to the sidewalk below.Write the position s(t),velocity v(t),and acceleration a(t)as functions of time.

Assume that x and y are differentiable functions of t.Find using the given values. for ,

The demand function for a product is modeled by What is the limit of the price as x increases without bound?

Find an equation of the tangent line to the graph of f at the given point. ,at

Solve the exponential equation.Give the answer correct to 3 decimal places.

Use the limit definition to find the slope of the tangent line to the graph of at the point

Which of the following is the correct graph of ?

Sketch a graph of a function f having the following characteristics.

If ,find

Solve for the equation for

Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places.

Use the point on a line having slope to find two additional points through which the line passes.

Find the derivative of the following function.

Find the slope of the graph at the given point.

Find the derivative of the following function using the limiting process.

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 graph f '' to sketch the graph of ​f​. ​ ​

To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.

These three points are collinear. ​ , , ​

​The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places. ​

​A brick becomes dislodged from the Empire State Building (at a height of 1,000 feet)and falls to the sidewalk below.Write the position s(t),velocity v(t),and acceleration a(t)as functions of time. ​

​Assume that x and y are differentiable functions of t.Find using the given values. ​ for , ​

The demand function for a product is modeled by What is the limit of the price as x increases without bound?

​Find an equation of the tangent line to the graph of f at the given point. ​ ,at ​

​Solve the exponential equation.Give the answer correct to 3 decimal places. ​ ​

​Use the limit definition to find the slope of the tangent line to the graph of at the point ​

​Which of the following is the correct graph of ? ​

​Sketch a graph of a function f having the following characteristics. ​ ​ ​

If ,find ​ ​

​Solve for the equation for ​

​Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places. ​ ​

Use the point on a line having slope to find two additional points through which the line passes. ​

​Find the derivative of the following function. ​ ​

​Find the slope of the graph at the given point. ​ ​ ​

​Find the derivative of the following function using the limiting process. ​ ​

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 graph f '' to sketch the graph of f.

These three points are collinear. , ,

The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places.

A brick becomes dislodged from the Empire State Building (at a height of 1,000 feet)and falls to the sidewalk below.Write the position s(t),velocity v(t),and acceleration a(t)as functions of time.

Assume that x and y are differentiable functions of t.Find using the given values. for ,

Find an equation of the tangent line to the graph of f at the given point. ,at

Solve the exponential equation.Give the answer correct to 3 decimal places.

Use the limit definition to find the slope of the tangent line to the graph of at the point

Which of the following is the correct graph of ?

Sketch a graph of a function f having the following characteristics.

If ,find

Solve for the equation for

Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places.

Use the point on a line having slope to find two additional points through which the line passes.

Find the derivative of the following function.

Find the slope of the graph at the given point.

Find the derivative of the following function using the limiting process.