Question 1

Complete the table and use the result to estimate the limit.Round your answer to six decimal places. ​   ​

Accepted Answer

A) 2.474874 
B) -2.349874 
C) -2.474874 
D) 2.308207 
E) 2.224874 
A) 2.474874 
B) -2.349874 
C) -2.474874 
D) 2.308207 
E) 2.224874 C

Question 2

​An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away   ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer. ​

Accepted Answer

A)  ​223 mi/hr 
B)  ​​206 mi/hr 
C)  ​446​ mi/hr 
D)  ​​111 mi/hr 
E)  ​​103 mi/hr 
A)  ​223 mi/hr 
B)  ​​206 mi/hr 
C)  ​446​ mi/hr 
D)  ​​111 mi/hr 
E)  ​​103 mi/hr A

Question 3

​Use the properties of logarithms to approximate   ,given that   ​

Accepted Answer

A)  ​-4.9767 
B)  ​-1.7579 
C)  ​0.4780 
D)  ​5.4195 
E)  ​4.9767 
A)  ​-4.9767 
B)  ​-1.7579 
C)  ​0.4780 
D)  ​5.4195 
E)  ​4.9767 B

Question 4

​Analyze and sketch a graph of the function   ​

Accepted Answer

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

Question 5

Assume that the number (in millions)of cellular telephone subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a line plot of the given data.Describe any trends that appear within the last four years. ​

Accepted Answer

A)  ​  
The number of subscribers appears to be increasing. 
B)  ​  
The number of subscribers appears to be decreasing. 
C)  ​  
The number of subscribers appears to be constant. 
D)  ​  
The number of subscribers appears to be decreasing 
E)  ​  
The number of subscribers appears to be increasing. 
A)  ​  
The number of subscribers appears to be increasing. 
B)  ​  
The number of subscribers appears to be decreasing. 
C)  ​  
The number of subscribers appears to be constant. 
D)  ​  
The number of subscribers appears to be decreasing 
E)  ​  
The number of subscribers appears to be increasing.

Question 6

​Sketch the graph of the function   ​

Accepted Answer

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

Question 7

Let   Determine the following limit.(Hint: Use the graph of the function.) ​   ​   ​ ​

Accepted Answer

A)  ​3 
B)  ​1 
C)  ​2 
D)  ​4 
E)  ​does not exist. 
A)  ​3 
B)  ​1 
C)  ​2 
D)  ​4 
E)  ​does not exist.

Question 8

​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 9

​Both a function and its derivative are given.Use them to find all critical numbers. ​
​   ​

Accepted Answer

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

Question 10

Find the points of intersection (if any)of the graphs of the equations       ​

Accepted Answer

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

Question 11

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

Accepted Answer

A)  343 
B)  0.571 
C)  0.712 
D)  0.356 
E)  0.805 
A)  343 
B)  0.571 
C)  0.712 
D)  0.356 
E)  0.805

Question 12

​Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand:   Supply:

Accepted Answer

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

Question 13

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 14

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly. ​

Accepted Answer

A)  $9,072.00 
B)  $4,799.87 
C)  $7,043.82 
D)  $7,122.70 
E)  $7,164.22 
A)  $9,072.00 
B)  $4,799.87 
C)  $7,043.82 
D)  $7,122.70 
E)  $7,164.22

Question 15

​Find an equation of the tangent line to the graph of   at the point   ​

Accepted Answer

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

Question 16

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

Accepted Answer

A)  ​2 
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​2 
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 17

​A point is moving along the graph of the function   such that   centimeters per second. Find   for the given values of x.
​   ​

Accepted Answer

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

Question 18

​The demand function for a product is modeled by   Find the price of the product if the quantity demanded is   Round your answer to two decimal places where applicable.

Accepted Answer

A)  ​$158.51 
B)  ​$2,468.78 
C)  ​$531.22 
D)  ​$2,478.98 
E)  ​$541.52 
A)  ​$158.51 
B)  ​$2,468.78 
C)  ​$531.22 
D)  ​$2,478.98 
E)  ​$541.52

Question 19

Write the logarithmic equation   as an exponential equation. ​

Accepted Answer

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

Question 20

​Analyze and sketch a graph of the function   ​

Accepted Answer

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

Complete the table and use the result to estimate the limit.Round your answer to six decimal places.

An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer.

Use the properties of logarithms to approximate ,given that

Analyze and sketch a graph of the function

Assume that the number (in millions)of cellular telephone subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a line plot of the given data.Describe any trends that appear within the last four years.

Sketch the graph of the function

Let Determine the following limit.(Hint: Use the graph of the function.)

Find any vertical asymptotes for the given function.

Both a function and its derivative are given.Use them to find all critical numbers.

Find the points of intersection (if any)of the graphs of the equations

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

Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand: Supply:

Find the derivative of the following function.

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly.

Find an equation of the tangent line to the graph of at the point

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

A point is moving along the graph of the function such that centimeters per second. Find for the given values of x.

The demand function for a product is modeled by Find the price of the product if the quantity demanded is Round your answer to two decimal places where applicable.

Write the logarithmic equation as an exponential equation.

Analyze and sketch a graph of the 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

Complete the table and use the result to estimate the limit.Round your answer to six decimal places. ​ ​

​An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer. ​

​Use the properties of logarithms to approximate ,given that ​

​Analyze and sketch a graph of the function ​

Assume that the number (in millions)of cellular telephone subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a line plot of the given data.Describe any trends that appear within the last four years. ​

​Sketch the graph of the function ​

Let Determine the following limit.(Hint: Use the graph of the function.) ​ ​ ​ ​

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

​Both a function and its derivative are given.Use them to find all critical numbers. ​ ​ ​

Find the points of intersection (if any)of the graphs of the equations ​

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

​Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand: Supply:

​Find the derivative of the following function. ​ ​

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly. ​

​Find an equation of the tangent line to the graph of at the point ​

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

​A point is moving along the graph of the function such that centimeters per second. Find for the given values of x. ​ ​

​The demand function for a product is modeled by Find the price of the product if the quantity demanded is Round your answer to two decimal places where applicable.

Write the logarithmic equation as an exponential equation. ​

​Analyze and sketch a graph of the 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

Complete the table and use the result to estimate the limit.Round your answer to six decimal places.

An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer.

Use the properties of logarithms to approximate ,given that

Analyze and sketch a graph of the function

Assume that the number (in millions)of cellular telephone subscribers in the United States from 1996 through 2005 is given in the following table.Use a graphing utility to graph a line plot of the given data.Describe any trends that appear within the last four years.

Sketch the graph of the function

Let Determine the following limit.(Hint: Use the graph of the function.)

Find any vertical asymptotes for the given function.

Both a function and its derivative are given.Use them to find all critical numbers.

Find the points of intersection (if any)of the graphs of the equations

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

Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand: Supply:

Find the derivative of the following function.

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly.

Find an equation of the tangent line to the graph of at the point

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

A point is moving along the graph of the function such that centimeters per second. Find for the given values of x.

The demand function for a product is modeled by Find the price of the product if the quantity demanded is Round your answer to two decimal places where applicable.

Write the logarithmic equation as an exponential equation.

Analyze and sketch a graph of the function