Question 1

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)    C

Question 2

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

Accepted Answer

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

Question 3

Solve the problem.
-One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees Fahrenheit) is given by   Approximate the changes in body temperature
Produced by changing the drug dosage from 1 to 1.8 milligrams. Round to the nearest hundredth when
Necessary.

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Provide an appropriate response.
-Use a graphing utility to approximate the partition numbers of the function to four decimal places:

Accepted Answer

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

Question 6

Describe the end behavior of the function.
-

Accepted Answer

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

Question 7

Provide an appropriate response.
-  , find the slope of the tangent line at x = 4.

Accepted Answer

A)  20 
B)  16 
C)  8 
D)  22 
A)  20 
B)  16 
C)  8 
D)  22

Question 8

Solve the problem.
-The cost of manufacturing a particular videotape is   where x is the number of tapes produced. The average cost per tape, denoted by   is found by dividing C(x) by x.

Accepted Answer

A)  14 
B)  6 
C)  10 
D)  Does not exist 
A)  14 
B)  6 
C)  10 
D)  Does not exist

Question 9

Provide an appropriate response.
-Use the four step process to find f'(x) for the function

Accepted Answer

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

Question 10

Solve the problem.
-If an object moves along a line so that it is at   at time x (in seconds), find the velocity at x = 1 (y is measured in feet).

Accepted Answer

A)  6 ft/sec 
B)  8 ft / s 
C)  16 ft / s 
D)  160 ft/s 
A)  6 ft/sec 
B)  8 ft / s 
C)  16 ft / s 
D)  160 ft/s

Question 11

Provide an appropriate response.
-Find:

Accepted Answer

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

Question 12

Find the limit, if it exists.
-Given

Accepted Answer

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

Question 13

Find the limit, if it exists.
-Let   Find

Accepted Answer

A)    
B)  4 
C)  -4 
D)  Does not exist 
A)    
B)  4 
C)  -4 
D)  Does not exist

Question 14

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

Accepted Answer

A)    is a vertical asymptote 
B)    6 is a vertical asymptote 
C)    is a vertical asymptote 
D)    is a vertical asymptote 
A)    is a vertical asymptote 
B)    6 is a vertical asymptote 
C)    is a vertical asymptote 
D)    is a vertical asymptote

Question 15

Provide an appropriate response.
-Find the vertical asymptote(s) of the graph of the given function.

Accepted Answer

A)  x = 9, x = -3 
B)  x = -9 
C)  x = 10, x = -10 
D)  y = 9, y = -3 
A)  x = 9, x = -3 
B)  x = -9 
C)  x = 10, x = -10 
D)  y = 9, y = -3

Question 16

Find the limit, if it exists.
-Let

Accepted Answer

A)  5 
B)  -7 
C)  -2 
D)  Does not exist 
A)  5 
B)  -7 
C)  -2 
D)  Does not exist

Question 17

List the x-values in the graph at which the function is not differentiable.
-

Accepted Answer

A)  x = -3, x = 0, x = 3 
B)  x = -2, x = 0, x = 2 
C)  x = -2, x = 2 
D)  x = -3, x = 3 
A)  x = -3, x = 0, x = 3 
B)  x = -2, x = 0, x = 2 
C)  x = -2, x = 2 
D)  x = -3, x = 3

Question 18

Use the given graph to find the indicated limit.
-

Accepted Answer

A)    
B)    
C)  4 
D)  3 
A)    
B)    
C)  4 
D)  3

Question 19

Use the definition   to find the derivative at x.
-f(x) = 13x - 12

Accepted Answer

A)  13x 
B)  1 
C)  13 
D)  -13 
A)  13x 
B)  1 
C)  13 
D)  -13

Question 20

Find the equation of the tangent line to the curve when x has the given value.
-

Accepted Answer

A)  y = 14x - 46 
B)  y = -14x + 46 
C)  y = 7x + 46 
D)  y = -2x 
A)  y = 14x - 46 
B)  y = -14x + 46 
C)  y = 7x + 46 
D)  y = -2x

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

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

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

Provide an appropriate response. -Use a graphing utility to approximate the partition numbers of the function to four decimal places:

Describe the end behavior of the function. -

Provide an appropriate response. - , find the slope of the tangent line at x = 4.

Solve the problem. -The cost of manufacturing a particular videotape is where x is the number of tapes produced. The average cost per tape, denoted by is found by dividing C(x) by x.

Provide an appropriate response. -Use the four step process to find f'(x) for the function

Solve the problem. -If an object moves along a line so that it is at at time x (in seconds), find the velocity at x = 1 (y is measured in feet).

Provide an appropriate response. -Find:

Find the limit, if it exists. -Given

Find the limit, if it exists. -Let Find

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

Provide an appropriate response. -Find the vertical asymptote(s) of the graph of the given function.

Find the limit, if it exists. -Let

List the x-values in the graph at which the function is not differentiable. -

Use the given graph to find the indicated limit. -

Use the definition to find the derivative at x. -f(x) = 13x - 12

Find the equation of the tangent line to the curve when x has the given value. -

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. -Use a sign chart to solve the inequality. Express answers in interval notation.

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

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

Provide an appropriate response. -Use a graphing utility to approximate the partition numbers of the function to four decimal places:

Describe the end behavior of the function. -

Provide an appropriate response. - , find the slope of the tangent line at x = 4.

Solve the problem. -The cost of manufacturing a particular videotape is where x is the number of tapes produced. The average cost per tape, denoted by is found by dividing C(x) by x.

Provide an appropriate response. -Use the four step process to find f'(x) for the function

Solve the problem. -If an object moves along a line so that it is at at time x (in seconds), find the velocity at x = 1 (y is measured in feet).

Provide an appropriate response. -Find:

Find the limit, if it exists. -Given

Find the limit, if it exists. -Let Find

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

Provide an appropriate response. -Find the vertical asymptote(s) of the graph of the given function.

Find the limit, if it exists. -Let

List the x-values in the graph at which the function is not differentiable. -

Use the given graph to find the indicated limit. -

Use the definition to find the derivative at x. -f(x) = 13x - 12

Find the equation of the tangent line to the curve when x has the given value. -

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