Question 1

​Use the properties of logarithms to write the expression   as a sum,difference,or multiple of logarithms.

Accepted Answer

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

Question 2

​Analyze and sketch a graph of the function   ​

Accepted Answer

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

Question 3

​Find the open intervals on which the function   is increasing or decreasing. ​

Accepted Answer

A)  ​The function is increasing on the interval   , and decreasing on the intervals   and   
B)  ​The function is increasing on the interval   , and decreasing on the intervals   and   
C)  ​​The function is increasing on the interval   , and decreasing on the intervals   and   
D)  ​The function is decreasing on the interval   , and increasing on the intervals   and   
E)  ​The function is decreasing on the interval   ,and increasing on the intervals   and   
A)  ​The function is increasing on the interval   , and decreasing on the intervals   and   
B)  ​The function is increasing on the interval   , and decreasing on the intervals   and   
C)  ​​The function is increasing on the interval   , and decreasing on the intervals   and   
D)  ​The function is decreasing on the interval   , and increasing on the intervals   and   
E)  ​The function is decreasing on the interval   ,and increasing on the intervals   and

Question 4

​Analyze and sketch a graph of the function   ​

Accepted Answer

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

Question 5

​The value V of a machine t years after it is purchased is inversely proportional to the square root of   The initial value of the machine is $10,000.Find the rate of depreciation when   Round your answer to two decimal places. ​

Accepted Answer

A)  -381.80 per year 
B)  ​-1,889.82 per year 
C)  ​447.21 per year 
D)  ​1,767.77 per year 
E)  -763.60​ per year 
A)  -381.80 per year 
B)  ​-1,889.82 per year 
C)  ​447.21 per year 
D)  ​1,767.77 per year 
E)  -763.60​ per year

Question 6

Find the slope of the tangent line to the graph of the function below at the given point. ​   ,   ​

Accepted Answer

A)  ​-12 
B)  ​-2 
C)  ​10 
D)  ​-18 
E)  ​none of the above 
A)  ​-12 
B)  ​-2 
C)  ​10 
D)  ​-18 
E)  ​none of the above

Question 7

​Identify the open intervals where the function   is increasing or decreasing. ​

Accepted Answer

A)  ​decreasing:   ; increasing:   
B)  ​increasing:   ; decreasing:   
C)  ​increasing:   ; decreasing:   
D)  ​increasing:   ; decreasing:   
E)  ​decreasing for all x 
A)  ​decreasing:   ; increasing:   
B)  ​increasing:   ; decreasing:   
C)  ​increasing:   ; decreasing:   
D)  ​increasing:   ; decreasing:   
E)  ​decreasing for all x

Question 8

​Find the slope m and y-intercept b of the line whose equation is given below. ​   ​

Accepted Answer

A)  ​   ,   
B)  ​​   ,   
C)    ,   
D)  ​   ,   
E)  Both m and b are undefined. 
A)  ​   ,   
B)  ​​   ,   
C)    ,   
D)  ​   ,   
E)  Both m and b are undefined.

Question 9

​Find the derivative of the function. ​
​   ​

Accepted Answer

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

Question 10

For the function   ​ (a)Find the critical numbers of f (if any);
(b)Find the open intervals where the function is increasing or decreasing; and
(c)Apply the First Derivative Test to identify all relative extrema.
​

Accepted Answer

A)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:  
​ 
B)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:  
​ 
C)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:  
​ 
D)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:  
​ 
E)  (a)  
(b)increasing:   ; decreasing:  
(c)relative max:   ; relative min: no relative min.
​ 
A)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:  
​ 
B)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:  
​ 
C)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:  
​ 
D)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:  
​ 
E)  (a)  
(b)increasing:   ; decreasing:  
(c)relative max:   ; relative min: no relative min.
​

Question 11

The cost of producing x units of a product is modeled by   Find the minimum average cost analytically.Round your answer to two decimal places. ​

Accepted Answer

A)  ​400.00 dollars per unit 
B)  ​381.19 dollars per unit 
C)  374.43​ dollars per unit 
D)  376.66​ dollars per unit 
E)  ​374.53 dollars per unit 
A)  ​400.00 dollars per unit 
B)  ​381.19 dollars per unit 
C)  374.43​ dollars per unit 
D)  376.66​ dollars per unit 
E)  ​374.53 dollars per unit

Question 12

​Use analytic methods to find the limit as   for the given function. ​
​   ​

Accepted Answer

A)  ​2500 
B)  ​2425 
C)  ​-2425 
D)  ​-2500 
E)  ​does not exist 
A)  ​2500 
B)  ​2425 
C)  ​-2425 
D)  ​-2500 
E)  ​does not exist

Question 13

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place. ​

Accepted Answer

A)  -24.1 feet/second 
B)  -0.2 feet/second 
C)  -0.6 feet/second 
D)  -15 feet/second 
E)  -0.9 feet/second 
A)  -24.1 feet/second 
B)  -0.2 feet/second 
C)  -0.6 feet/second 
D)  -15 feet/second 
E)  -0.9 feet/second

Question 14

​Find the derivative of the function   State which differentiation rule(s)you used to find the derivative. ​

Accepted Answer

A)  ​1, Product Rule. 
B)  ​1, Quotient Rule. 
C)  ​5, Product Rule. 
D)  ​5, Quotient Rule. 
E)  ​   ,Product Rule. 
A)  ​1, Product Rule. 
B)  ​1, Quotient Rule. 
C)  ​5, Product Rule. 
D)  ​5, Quotient Rule. 
E)  ​   ,Product Rule.

Question 15

​The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer. ​

Accepted Answer

A)  ​10 bacteria 
B)  903 ​bacteria 
C)  ​1,008 bacteria 
D)  ​23 bacteria 
E)  ​18 bacteria 
A)  ​10 bacteria 
B)  903 ​bacteria 
C)  ​1,008 bacteria 
D)  ​23 bacteria 
E)  ​18 bacteria

Question 16

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

Accepted Answer

A)  ​-0.219 
B)  ​2.033 
C)  ​0.274 
D)  ​-2.033 
E)  ​-0.224 
A)  ​-0.219 
B)  ​2.033 
C)  ​0.274 
D)  ​-2.033 
E)  ​-0.224

Question 17

​Use the properties of logarithms to expand

Accepted Answer

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

Question 18

​Write the equation of the line tangent to the curve   at the point (2,1). ​

Accepted Answer

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

Question 19

Find constants a and b such that the function   is continuous on the entire real line. ​

Accepted Answer

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

Question 20

​Use the Vertical Line Test to determine which of the following graphs shows y as a function of x. ​

Accepted Answer

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

Use the properties of logarithms to write the expression as a sum,difference,or multiple of logarithms.

Analyze and sketch a graph of the function

Find the open intervals on which the function is increasing or decreasing.

Analyze and sketch a graph of the function

The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places.

Find the slope of the tangent line to the graph of the function below at the given point. ,

Identify the open intervals where the function is increasing or decreasing.

Find the slope m and y-intercept b of the line whose equation is given below.

Find the derivative of the function.

For the function (a)Find the critical numbers of f (if any); (b)Find the open intervals where the function is increasing or decreasing; and (c)Apply the First Derivative Test to identify all relative extrema.

The cost of producing x units of a product is modeled by Find the minimum average cost analytically.Round your answer to two decimal places.

Use analytic methods to find the limit as for the given function.

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.

Find the derivative of the function State which differentiation rule(s)you used to find the derivative.

The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer.

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

Use the properties of logarithms to expand

Write the equation of the line tangent to the curve at the point (2,1).

Find constants a and b such that the function is continuous on the entire real line.

Use the Vertical Line Test to determine which of the following graphs shows y as a function of x.

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 sum,difference,or multiple of logarithms.

​Analyze and sketch a graph of the function ​

​Find the open intervals on which the function is increasing or decreasing. ​

​Analyze and sketch a graph of the function ​

​The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places. ​

Find the slope of the tangent line to the graph of the function below at the given point. ​ , ​

​Identify the open intervals where the function is increasing or decreasing. ​

​Find the slope m and y-intercept b of the line whose equation is given below. ​ ​

​Find the derivative of the function. ​ ​ ​

For the function ​ (a)Find the critical numbers of f (if any); (b)Find the open intervals where the function is increasing or decreasing; and (c)Apply the First Derivative Test to identify all relative extrema. ​

The cost of producing x units of a product is modeled by Find the minimum average cost analytically.Round your answer to two decimal places. ​

​Use analytic methods to find the limit as for the given function. ​ ​ ​

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place. ​

​Find the derivative of the function State which differentiation rule(s)you used to find the derivative. ​

​The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer. ​

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

​Use the properties of logarithms to expand

​Write the equation of the line tangent to the curve at the point (2,1). ​

Find constants a and b such that the function is continuous on the entire real line. ​

​Use the Vertical Line Test to determine which of the following graphs shows y as a function of x. ​

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 sum,difference,or multiple of logarithms.

Analyze and sketch a graph of the function

Find the open intervals on which the function is increasing or decreasing.

Analyze and sketch a graph of the function

The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places.

Find the slope of the tangent line to the graph of the function below at the given point. ,

Identify the open intervals where the function is increasing or decreasing.

Find the slope m and y-intercept b of the line whose equation is given below.

Find the derivative of the function.

For the function (a)Find the critical numbers of f (if any); (b)Find the open intervals where the function is increasing or decreasing; and (c)Apply the First Derivative Test to identify all relative extrema.

The cost of producing x units of a product is modeled by Find the minimum average cost analytically.Round your answer to two decimal places.

Use analytic methods to find the limit as for the given function.

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.

Find the derivative of the function State which differentiation rule(s)you used to find the derivative.

The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer.

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

Use the properties of logarithms to expand

Write the equation of the line tangent to the curve at the point (2,1).

Find constants a and b such that the function is continuous on the entire real line.

Use the Vertical Line Test to determine which of the following graphs shows y as a function of x.