Question 1

Find the instantaneous rate of change for the function at the value given.
-Find the instantaneous rate of change for the function

Accepted Answer

A)  120 
B)  15 
C)  23 
D)  16 
A)  120 
B)  15 
C)  23 
D)  16

Question 2

Solve the problem.
-Suppose the demand for a certain item is given by   where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

Accepted Answer

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

Question 3

Solve the problem.
-A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by:   Find the marginal cost at a production level of 70 dozen pens and interpret the result.

Accepted Answer

A)  The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.59. 
B)  The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.60. 
C)  The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.58. 
D)  The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.62. 
A)  The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.59. 
B)  The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.60. 
C)  The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.58. 
D)  The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.62.

Question 4

Provide an appropriate response.
-Use the four step p

Accepted Answer

A)  10x + 5h - 3 
B)    
C)  5h - 3 
D)  10x - 3 
A)  10x + 5h - 3 
B)    
C)  5h - 3 
D)  10x - 3

Question 5

Find average rate of change for the function over the given interval.
-Find the average rate of change for   if x changes from 2 to 8.

Accepted Answer

A)  7 
B)    
C)    
D)  2 
A)  7 
B)    
C)    
D)  2

Question 6

Use -∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical
asymptotes.
-

Accepted Answer

A)  No zeros of denominator; no vertical asymptotes 
B)    is a vertical asymptote 
C)    is a vertical asymptote 
D)    is a vertical asymptote 
A)  No zeros of denominator; no vertical asymptotes 
B)    is a vertical asymptote 
C)    is a vertical asymptote 
D)    is a vertical asymptote

Question 7

Find the limit, if it exists.
-Find:

Accepted Answer

A)  - 24 
B)  8 
C)  -8 
D)  16 
A)  - 24 
B)  8 
C)  -8 
D)  16

Question 8

Solve the problem.
-An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by   Find the velocity at three seconds.

Accepted Answer

A)  190 feet per second 
B)  109 feet per second 
C)  192 feet per second 
D)  197 feet per second 
A)  190 feet per second 
B)  109 feet per second 
C)  192 feet per second 
D)  197 feet per second

Question 9

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

Accepted Answer

A)  100 
B)  30 
C)  70 
D)  85 
A)  100 
B)  30 
C)  70 
D)  85

Question 10

Use the graph to evaluate the indicated limit and function value or state that it does not exist.
-Find

Accepted Answer

A)  -1; 5 
B)  5; -1 
C)  5; Does not exist 
D)  Does not exist; does not exist 
A)  -1; 5 
B)  5; -1 
C)  5; Does not exist 
D)  Does not exist; does not exist

Question 11

Provide an appropriate response.
-If the limit at infinity exists, find the limit.

Accepted Answer

A)    
B)  1 
C)    
D)  0 
A)    
B)  1 
C)    
D)  0

Question 12

Provide an appropriate response.
-Find the values of x where the tangent line is horizontal for

Accepted Answer

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

Question 13

Provide an appropriate response.
-Use a sign chart to solve the inequality. Express answers in interval notation.

Accepted Answer

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

Question 14

Provide an appropriate response.
-Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for

Accepted Answer

A)  55 
B)  15 
C)  -55 
D)  -15 
A)  55 
B)  15 
C)  -55 
D)  -15

Question 15

Find the limit, if it exists.
-Find:

Accepted Answer

A)  1 
B)  0 
C)  -1 
D)  Does not exist 
A)  1 
B)  0 
C)  -1 
D)  Does not exist

Question 16

Provide an appropriate response.
-Find

Accepted Answer

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

Question 17

Solve the problem.
-According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by:   Find the rate of learning at the end of eight hours of instruction.

Accepted Answer

A)  20 items per hour 
B)  45 items per hour 
C)  5 items per hour 
D)  60 items per hour 
A)  20 items per hour 
B)  45 items per hour 
C)  5 items per hour 
D)  60 items per hour

Question 18

Provide an appropriate response.
-Find the slope of the line tangent to the graph of the function at the given value of x.

Accepted Answer

A)  65 
B)  -52 
C)  -50 
D)  67 
A)  65 
B)  -52 
C)  -50 
D)  67

Question 19

Solve the problem.
-The cost of renting a snowblower is $20 for the first hour (or any fraction thereof) and $5 for each additional hour (or fraction thereof) up to a maximum rental time of 5 hours. Write a piecewise definition of the cost C(x)
Of renting a snowblower for x hours. Is C(x) continuous at x = 2.5?

Accepted Answer

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

Question 20

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

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function

Solve the problem. -Suppose the demand for a certain item is given by where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

Solve the problem. -A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: Find the marginal cost at a production level of 70 dozen pens and interpret the result.

Provide an appropriate response. -Use the four step p

Find average rate of change for the function over the given interval. -Find the average rate of change for if x changes from 2 to 8.

Use -∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. -

Find the limit, if it exists. -Find:

Solve the problem. -An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by Find the velocity at three seconds.

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

Use the graph to evaluate the indicated limit and function value or state that it does not exist. -Find

Provide an appropriate response. -If the limit at infinity exists, find the limit.

Provide an appropriate response. -Find the values of x where the tangent line is horizontal for

Provide an appropriate response. -Use a sign chart to solve the inequality. Express answers in interval notation.

Provide an appropriate response. -Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for

Find the limit, if it exists. -Find:

Provide an appropriate response. -Find

Solve the problem. -According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by: Find the rate of learning at the end of eight hours of instruction.

Provide an appropriate response. -Find the slope of the line tangent to the graph of the function at the given value of x.

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

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

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function

Solve the problem. -Suppose the demand for a certain item is given by where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

Solve the problem. -A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: Find the marginal cost at a production level of 70 dozen pens and interpret the result.

Provide an appropriate response. -Use the four step p

Find average rate of change for the function over the given interval. -Find the average rate of change for if x changes from 2 to 8.

Use -∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. -

Find the limit, if it exists. -Find:

Solve the problem. -An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by Find the velocity at three seconds.

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

Use the graph to evaluate the indicated limit and function value or state that it does not exist. -Find

Provide an appropriate response. -If the limit at infinity exists, find the limit.

Provide an appropriate response. -Find the values of x where the tangent line is horizontal for

Provide an appropriate response. -Use a sign chart to solve the inequality. Express answers in interval notation.

Provide an appropriate response. -Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for

Find the limit, if it exists. -Find:

Provide an appropriate response. -Find

Solve the problem. -According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by: Find the rate of learning at the end of eight hours of instruction.

Provide an appropriate response. -Find the slope of the line tangent to the graph of the function at the given value of x.

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

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