Question 1

If the revenue for a product (in dollars) is   and the average revenue per unit is   ,   , find   . ​

Accepted Answer

A)  $520 per unit 
B)  $545 per unit 
C)  $530 per unit 
D)  $0 per unit 
E)  does not exist 
A)  $520 per unit 
B)  $545 per unit 
C)  $530 per unit 
D)  $0 per unit 
E)  does not exist

Question 2

Determine whether the given function   is continuous. If   is not continuous, identify where it is discontinuous and which condition(s) fails to hold. ​

Accepted Answer

A)    is discontinuous at   since   is not defined and   does not exist. 
B)    is discontinuous at   since   is not defined and   does not exist. 
C)    is discontinuous at   since   is not defined and   does not exist. 
D)    is continuous. 
E)    is discontinuous at   since   is not defined and   does not exist. 
A)    is discontinuous at   since   is not defined and   does not exist. 
B)    is discontinuous at   since   is not defined and   does not exist. 
C)    is discontinuous at   since   is not defined and   does not exist. 
D)    is continuous. 
E)    is discontinuous at   since   is not defined and   does not exist.

Question 3

For the given function, find the average rate of change over the specified interval. ​   over   ​

Accepted Answer

A)  0 
B)  4 
C)  2 
D)  -17 
E)  17 
A)  0 
B)  4 
C)  2 
D)  -17 
E)  17

Question 4

Use the graph of   and the given c-value to find   . ​   ​   ​

Accepted Answer

A)  2 
B)  -2 
C)  6 
D)  0 
E)  does not exist 
A)  2 
B)  -2 
C)  6 
D)  0 
E)  does not exist

Question 5

For the given function, find the instantaneous rate of change at   . A graphing utility's numerical derivative feature may be used to check your work. ​   ​

Accepted Answer

A)  8 
B)  3 
C)  24 
D)  96 
E)  30 
A)  8 
B)  3 
C)  24 
D)  96 
E)  30

Question 6

Find   for the given function. ​   ​

Accepted Answer

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

Question 7

Use properties of limits and algebraic methods to find the limit, if it exists. ​   ​

Accepted Answer

A)    
B)  -3 
C)    
D)    
E)  does not exist 
A)    
B)  -3 
C)    
D)    
E)  does not exist

Question 8

Find the indicated derivative. Find   ​

Accepted Answer

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

Question 9

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function   .
Is C continuous at   ?
​

Accepted Answer

A) True 
 B)False

Question 10

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is   Find   , and tell what it represents. ​

Accepted Answer

A)  $9.60. This represents the revenue from the sale of 40 units. 
B)  $478.80. This represents the marginal revenue from the sale of 40 units. 
C)  $480.00. This represents the marginal revenue from the sale of 40 units. 
D)  $432.00. This represents the revenue from the sale of 40 units. 
E)  $1.20. This represents the revenue from the sale of 40 units. 
A)  $9.60. This represents the revenue from the sale of 40 units. 
B)  $478.80. This represents the marginal revenue from the sale of 40 units. 
C)  $480.00. This represents the marginal revenue from the sale of 40 units. 
D)  $432.00. This represents the revenue from the sale of 40 units. 
E)  $1.20. This represents the revenue from the sale of 40 units.

Question 11

For the function given, find all x-values where   . ​   ​

Accepted Answer

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

Question 12

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

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

Question 13

The monthly output of a certain product is   where x is the capital investment in millions of dollars. Find   which can be used to estimate the effect on the output if an additional capital investment of $1 million is made. ​

Accepted Answer

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

Question 14

Use the graph of   and the given c-value to find   . ​   ​   ​

Accepted Answer

A)  -6 
B)  0 
C)  2 
D)  6 
E)  does not exist 
A)  -6 
B)  0 
C)  2 
D)  6 
E)  does not exist

Question 15

Determine whether the given function is continuous. If it is not, identify where it is discontinuous. ​   ​

Accepted Answer

A)  discontinuous at   
B)  discontinuous at   
C)  discontinuous at   
D)  discontinuous at   
E)  continuous everywhere 
A)  discontinuous at   
B)  discontinuous at   
C)  discontinuous at   
D)  discontinuous at   
E)  continuous everywhere

Question 16

Use properties of limits and algebraic methods to find the limit, if it exists. ​   ​

Accepted Answer

A)  0 
B)  -2 
C)  2 
D)  ​7 
E)  does not exist 
A)  0 
B)  -2 
C)  2 
D)  ​7 
E)  does not exist

Question 17

The tangent line to the graph of f (x) at   is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find   . ​   ​

Accepted Answer

A)  2 
B)  -2 
C)  1 
D)  -5 
E)  does not exist 
A)  2 
B)  -2 
C)  1 
D)  -5 
E)  does not exist

Question 18

Find   ​   ​

Accepted Answer

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

Question 19

A certain calling card costs 5.2 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 52 cent connection fee. If   is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. ​   ​

Accepted Answer

A)  $0 
B)  $0.45 
C)  $0.57 
D)  $0.44 
E)  does not exist 
A)  $0 
B)  $0.45 
C)  $0.57 
D)  $0.44 
E)  does not exist

Question 20

The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x according to the equation   how fast is the rate of change of photosynthesis with respect to the intensity changing when   ​

Accepted Answer

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

If the revenue for a product (in dollars) is and the average revenue per unit is , , find .

Determine whether the given function is continuous. If is not continuous, identify where it is discontinuous and which condition(s) fails to hold.

For the given function, find the average rate of change over the specified interval. over

Use the graph of and the given c-value to find .

For the given function, find the instantaneous rate of change at . A graphing utility's numerical derivative feature may be used to check your work.

Find for the given function.

Use properties of limits and algebraic methods to find the limit, if it exists.

Find the indicated derivative. Find

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function . Is C continuous at ?

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find , and tell what it represents.

For the function given, find all x-values where .

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

The monthly output of a certain product is where x is the capital investment in millions of dollars. Find which can be used to estimate the effect on the output if an additional capital investment of $1 million is made.

Use the graph of and the given c-value to find .

Determine whether the given function is continuous. If it is not, identify where it is discontinuous.

Use properties of limits and algebraic methods to find the limit, if it exists.

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find .

Find

The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x according to the equation how fast is the rate of change of photosynthesis with respect to the intensity changing when

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

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Exam 9: Derivatives

If the revenue for a product (in dollars) is and the average revenue per unit is , , find . ​

Determine whether the given function is continuous. If is not continuous, identify where it is discontinuous and which condition(s) fails to hold. ​

For the given function, find the average rate of change over the specified interval. ​ over ​

Use the graph of and the given c-value to find . ​ ​ ​

For the given function, find the instantaneous rate of change at . A graphing utility's numerical derivative feature may be used to check your work. ​ ​

Find for the given function. ​ ​

Use properties of limits and algebraic methods to find the limit, if it exists. ​ ​

Find the indicated derivative. Find ​

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function . Is C continuous at ? ​

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find , and tell what it represents. ​

For the function given, find all x-values where . ​ ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

The monthly output of a certain product is where x is the capital investment in millions of dollars. Find which can be used to estimate the effect on the output if an additional capital investment of $1 million is made. ​

Use the graph of and the given c-value to find . ​ ​ ​

Determine whether the given function is continuous. If it is not, identify where it is discontinuous. ​ ​

Use properties of limits and algebraic methods to find the limit, if it exists. ​ ​

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find . ​ ​

Find ​ ​

The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x according to the equation how fast is the rate of change of photosynthesis with respect to the intensity changing when ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

If the revenue for a product (in dollars) is and the average revenue per unit is , , find .

Determine whether the given function is continuous. If is not continuous, identify where it is discontinuous and which condition(s) fails to hold.

For the given function, find the average rate of change over the specified interval. over

Use the graph of and the given c-value to find .

For the given function, find the instantaneous rate of change at . A graphing utility's numerical derivative feature may be used to check your work.

Find for the given function.

Use properties of limits and algebraic methods to find the limit, if it exists.

Find the indicated derivative. Find

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function . Is C continuous at ?

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find , and tell what it represents.

For the function given, find all x-values where .

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

The monthly output of a certain product is where x is the capital investment in millions of dollars. Find which can be used to estimate the effect on the output if an additional capital investment of $1 million is made.

Use the graph of and the given c-value to find .

Determine whether the given function is continuous. If it is not, identify where it is discontinuous.

Use properties of limits and algebraic methods to find the limit, if it exists.

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find .

Find

The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x according to the equation how fast is the rate of change of photosynthesis with respect to the intensity changing when