Question 1

Provide an appropriate response.
-The revenue (in thousands of dollars) from producing x units of an item is modeled R   Find the marginal revenue at x = 1000.

Accepted Answer

A)  $4.50 
B)  $104.00 
C)  $4.00 
D)  $10,300.00 
A)  $4.50 
B)  $104.00 
C)  $4.00 
D)  $10,300.00

Question 2

Find the limit, if it exists.
-Evaluate the following limit.

Accepted Answer

A)  2 
B)    
C)    
D)  Does not exist 
A)  2 
B)    
C)    
D)  Does not exist

Question 3

Solve the problem.
-A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where

Accepted Answer

A)  42 
B)  105 
C)  30 
D)  Does not exist 
A)  42 
B)  105 
C)  30 
D)  Does not exist

Question 4

Provide an appropriate response.
-Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 5

Solve the problem.
-Suppose an object moves along the y-axis so that its location is   at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to
9 seconds.

Accepted Answer

A)  12 m/s 
B)  3 m/s 
C)  15 m/s 
D)  84 m/s 
A)  12 m/s 
B)  3 m/s 
C)  15 m/s 
D)  84 m/s

Question 6

Provide an appropriate response.
-The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost function.

Accepted Answer

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

Question 7

Find   for the given values of  
-

Accepted Answer

A)  1 
B)  0.5 
C)  0.1 
D)  5 
A)  1 
B)  0.5 
C)  0.1 
D)  5

Question 8

Sketch a possible graph of a function that satisfies the given conditions.
-f(1) = 4;

Accepted Answer

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

Question 9

Provide an appropriate response.
-Use a graphing utility to find the discontinuities of the given rational function.

Accepted Answer

A)  1 
B)  3 
C)  -1 
D)  Continuous at all values of x 
A)  1 
B)  3 
C)  -1 
D)  Continuous at all values of x

Question 10

Solve the problem.
-If an object moves along a line so that it is at   at time x (in seconds), find the instantaneous velocity function

Accepted Answer

A)  3x - 2 
B)  6x - 2 
C)    
D)    
A)  3x - 2 
B)  6x - 2 
C)    
D)

Question 11

Solve the problem.
-A cube 4 inches on an edge is given a protective coating 0.2 inches thick. About how much coating should a production manager order for 800 cubes?

Accepted Answer

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

Question 12

Solve the problem.
-Suppose an object moves along the y-axis so that its location is   at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

Accepted Answer

A)  9 m/s 
B)  10 m/s 
C)  8 m/s 
D)  20 m/s 
A)  9 m/s 
B)  10 m/s 
C)  8 m/s 
D)  20 m/s

Question 13

Provide an appropriate response.
-Find:

Accepted Answer

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

Question 14

Solve the problem.
-The demand equation for a certain item is   and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

Accepted Answer

A)  $7; at the 3,000 level of production, profit will increase by approximately $7 for each unit increase in production. 
B)  $16; at the 3,000 level of production, profit will increase by approximately $16 for each unit increase in production. 
C)  $14; at the 3,000 level of production, profit will increase by approximately $14 for each unit increase in production. 
D)  $4; at the 3,000 level of production, profit will increase by approximately $4 for each unit increase in production. 
A)  $7; at the 3,000 level of production, profit will increase by approximately $7 for each unit increase in production. 
B)  $16; at the 3,000 level of production, profit will increase by approximately $16 for each unit increase in production. 
C)  $14; at the 3,000 level of production, profit will increase by approximately $14 for each unit increase in production. 
D)  $4; at the 3,000 level of production, profit will increase by approximately $4 for each unit increase in production.

Question 15

Solve the problem.
-Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by   Can a company afford to remove 100% of the pollutants? Explain.

Accepted Answer

A)  Yes, the cost of removing p% of the pollutants is $400, which is certainly affordable. 
B)  No, the cost of removing p% of the pollutants is $400, which is a prohibitive amount of money. 
C)  Yes, the cost of removing p% of the pollutants is $40,000, which is certainly affordable. 
D)  No, the cost of removing p% of the pollutants increases without bound as p approaches 100. 
A)  Yes, the cost of removing p% of the pollutants is $400, which is certainly affordable. 
B)  No, the cost of removing p% of the pollutants is $400, which is a prohibitive amount of money. 
C)  Yes, the cost of removing p% of the pollutants is $40,000, which is certainly affordable. 
D)  No, the cost of removing p% of the pollutants increases without bound as p approaches 100.

Question 16

Sketch a possible graph of a function that satisfies the given conditions.
-

Accepted Answer

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

Question 17

Solve the problem.
-Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where

Accepted Answer

A)  16 
B)  23 
C)  7 
D)  19 
A)  16 
B)  23 
C)  7 
D)  19

Question 18

Find the limit, if it exists.
-Find:

Accepted Answer

A)  3 
B)  10 
C)  2 
D)  Does not exist 
A)  3 
B)  10 
C)  2 
D)  Does not exist

Question 19

Provide an appropriate response.
-Find

Accepted Answer

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

Question 20

The graph of y = f(x) is shown. Use the graph to answer the question.
-

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Provide an appropriate response. -The revenue (in thousands of dollars) from producing x units of an item is modeled R Find the marginal revenue at x = 1000.

Find the limit, if it exists. -Evaluate the following limit.

Solve the problem. -A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where

Provide an appropriate response. -Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.

Solve the problem. -Suppose an object moves along the y-axis so that its location is at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

Provide an appropriate response. -The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost function.

Find for the given values of -

Sketch a possible graph of a function that satisfies the given conditions. -f(1) = 4;

Provide an appropriate response. -Use a graphing utility to find the discontinuities of the given rational function.

Solve the problem. -If an object moves along a line so that it is at at time x (in seconds), find the instantaneous velocity function

Solve the problem. -A cube 4 inches on an edge is given a protective coating 0.2 inches thick. About how much coating should a production manager order for 800 cubes?

Solve the problem. -Suppose an object moves along the y-axis so that its location is at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

Provide an appropriate response. -Find:

Solve the problem. -The demand equation for a certain item is and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

Solve the problem. -Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by Can a company afford to remove 100% of the pollutants? Explain.

Sketch a possible graph of a function that satisfies the given conditions. -

Solve the problem. -Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where

Find the limit, if it exists. -Find:

Provide an appropriate response. -Find

The graph of y = f(x) is shown. Use the graph to answer the question. -

Functions and Graphs

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters

Exam 2: Limits and the Derivative

Provide an appropriate response. -The revenue (in thousands of dollars) from producing x units of an item is modeled R Find the marginal revenue at x = 1000.

Find the limit, if it exists. -Evaluate the following limit.

Solve the problem. -A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where

Provide an appropriate response. -Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.

Solve the problem. -Suppose an object moves along the y-axis so that its location is at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

Provide an appropriate response. -The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost function.

Find for the given values of -

Sketch a possible graph of a function that satisfies the given conditions. -f(1) = 4;

Provide an appropriate response. -Use a graphing utility to find the discontinuities of the given rational function.

Solve the problem. -If an object moves along a line so that it is at at time x (in seconds), find the instantaneous velocity function

Solve the problem. -A cube 4 inches on an edge is given a protective coating 0.2 inches thick. About how much coating should a production manager order for 800 cubes?

Solve the problem. -Suppose an object moves along the y-axis so that its location is at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

Provide an appropriate response. -Find:

Solve the problem. -The demand equation for a certain item is and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

Solve the problem. -Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by Can a company afford to remove 100% of the pollutants? Explain.

Sketch a possible graph of a function that satisfies the given conditions. -

Solve the problem. -Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where

Find the limit, if it exists. -Find:

Provide an appropriate response. -Find

The graph of y = f(x) is shown. Use the graph to answer the question. -

Functions and Graphs

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters