Question 1

L'Hopital's rule does not help with the given limit. Find the limit some other way.
-

Accepted Answer

A)  1 
B)  - 1 
C)  0 
D) $\infty$ 
A)  1 
B)  - 1 
C)  0 
D) $\infty$

Question 2

Find an antiderivative of the given function. 
-

Accepted Answer

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

Question 3

Graph the equation. Include the coordinates of any local extreme points and inflection points.
-y = 2x3 - 15x2 + 24x

Accepted Answer

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

Question 4

L'Hopital's rule does not help with the given limit. Find the limit some other way.
-

Accepted Answer

A)  $\infty$ 
B)  0 
C)  1 
D)  -1 
A)  $\infty$ 
B)  0 
C)  1 
D)  -1

Question 5

Find the most general antiderivative.      
-  dx

Accepted Answer

A)    + C 
B)  -3 tan x + C 
C)  3 cot x + C 
D)  -3 cot x + C 
A)    + C 
B)  -3 tan x + C 
C)  3 cot x + C 
D)  -3 cot x + C

Question 6

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y = 3   -

Accepted Answer

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

Question 7

Use Newton's method to find an approximate answer to the question. Round to six decimal places.
-Where are the inflection points of f(x) =     +     - 5   + 3 located?

Accepted Answer

A)  x $\approx$ -0.988578, 0.321912 
B)  x $\approx$ -1.100923, 0.933023 
C)  x$\approx$ -1.099689, 0.433023 
D)  x $\approx$ -0.849689, 0.683023 
A)  x $\approx$ -0.988578, 0.321912 
B)  x $\approx$ -1.100923, 0.933023 
C)  x$\approx$ -1.099689, 0.433023 
D)  x $\approx$ -0.849689, 0.683023

Question 8

Find an antiderivative of the given function. 
-9 cos 8x

Accepted Answer

A)  9 sin 8x 
B)  sin 8x 
C)  - 72 sin 8x 
D)    sin 8x 
A)  9 sin 8x 
B)  sin 8x 
C)  - 72 sin 8x 
D)    sin 8x

Question 9

Find the value or values of c that satisfy the equation   =   (c) in the conclusion of the Mean Value Theorem for the function and interval.
-f(x) =   x, [-1, 1]

Accepted Answer

A)  c = 0,   
B)  c = -   ,   
C)  c =   
D)  c = -   , 0 ,   
A)  c = 0,   
B)  c = -   ,   
C)  c =   
D)  c = -   , 0 ,

Question 10

Choose the one alternative that best completes the statement or answers the question.
-The graph below shows the first derivative of a function y = f(x). Select a possible graph of f that passes through the point P.

Accepted Answer

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

Question 11

Use differentiation to determine whether the integral formula is correct.
-

Accepted Answer

A) True 
 B)False

Question 12

Choose the one alternative that best completes the statement or answers the question. 
-If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x) = 17 -   . How many candy bars must be sold to maximize revenue?

Accepted Answer

A)  119 candy bars 
B)  238 candy bars 
C)  119 thousand candy bars 
D)  238 thousand candy bars 
A)  119 candy bars 
B)  238 candy bars 
C)  119 thousand candy bars 
D)  238 thousand candy bars

Question 13

For the given expression   , find y'' and sketch the general shape of the graph of y = f(x).
-  =   (x - 5)

Accepted Answer

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

Question 14

Find an antiderivative of the given function. 
-24   - 16x - 8

Accepted Answer

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

Question 15

Express the relationship between a small change in x and the corresponding change in y in the form   . 
-y = csc( 5   - 1)

Accepted Answer

A)  dy = -10x csc( 10x) cot( 10x) dx 
B)  
  
C)  
  
D)  
  
A)  dy = -10x csc( 10x) cot( 10x) dx 
B)  
  
C)  
  
D)

Question 16

Solve the problem.
-From a thin piece of cardboard 50 in. by 50 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

Accepted Answer

A)  16.7 in. × 16.7 in. × 16.7 in.; 4629.6   
B)  25 in. × 25 in. × 12.5 in.; 7812.5   
C)  33.3 in. × 33.3 in. × 8.3 in.; 9259.3   
D)  33.3 in. × 33.3 in. × 16.7 in.; 18,518.5   
A)  16.7 in. × 16.7 in. × 16.7 in.; 4629.6   
B)  25 in. × 25 in. × 12.5 in.; 7812.5   
C)  33.3 in. × 33.3 in. × 8.3 in.; 9259.3   
D)  33.3 in. × 33.3 in. × 16.7 in.; 18,518.5

Question 17

Provide an appropriate response.  
-Suppose the velocity of a body moving along the s-axis is   = 9.8t - 6. Is it necessary to know the initial position of the body to find the body's displacement over some time interval? Justify your answer.

Accepted Answer

A)  No, the initial position is necessary to find the curve s= f(t) but not necessary to find the displacement. The initial position determines the integration constant. When finding the displacement the integration constant is subtracted out. 
B)  No, displacement has nothing to do with the position of the body. 
C)  Yes, knowing the initial position is the only way to find the exact positions at the beginning and end of the time interval. Those positions are needed to find the displacement. 
D)  Yes, integration is not possible without knowing the initial position. 
A)  No, the initial position is necessary to find the curve s= f(t) but not necessary to find the displacement. The initial position determines the integration constant. When finding the displacement the integration constant is subtracted out. 
B)  No, displacement has nothing to do with the position of the body. 
C)  Yes, knowing the initial position is the only way to find the exact positions at the beginning and end of the time interval. Those positions are needed to find the displacement. 
D)  Yes, integration is not possible without knowing the initial position.

Question 18

Write the word or phrase that best completes each statement or answers the question. -Sketch a continuous curve y = f(x) with the following properties: f(2) = 3; (x) > 0 for x > 4; and (x) < 0 for x < 4 .

Accepted Answer

Answers will vary. A

Question 19

Find the largest open interval where the function is changing as requested.
-Decreasing f(x) = -

Accepted Answer

A)  (3, $\infty$) 
B)  (-3, $\infty$) 
C)  (-$\infty$, 3) 
D)  (-$\infty$, -3) 
A)  (3, $\infty$) 
B)  (-3, $\infty$) 
C)  (-$\infty$, 3) 
D)  (-$\infty$, -3)

Question 20

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places.
-f(x) = csc x - 2x on [0, 4]

Accepted Answer

A)  x $\approx$ 0.740730, 2.972474 
B)  x $\approx$ 0.850841, 3.082585 
C)  x $\approx$0.850852, 2.862574 
D)  x $\approx$ 0.740841, 2.972585 
A)  x $\approx$ 0.740730, 2.972474 
B)  x $\approx$ 0.850841, 3.082585 
C)  x $\approx$0.850852, 2.862574 
D)  x $\approx$ 0.740841, 2.972585

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Find an antiderivative of the given function. -

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = 2x³ - 15x² + 24x

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Find the most general antiderivative. - dx

Express the relationship between a small change in x and the corresponding change in y in the form . -y = 3 -

Use Newton's method to find an approximate answer to the question. Round to six decimal places. -Where are the inflection points of f(x) = + - 5 + 3 located?

Find an antiderivative of the given function. -9 cos 8x

Find the value or values of c that satisfy the equation = (c) in the conclusion of the Mean Value Theorem for the function and interval. -f(x) = x, [-1, 1]

Choose the one alternative that best completes the statement or answers the question. -The graph below shows the first derivative of a function y = f(x). Select a possible graph of f that passes through the point P.

Use differentiation to determine whether the integral formula is correct. -

Choose the one alternative that best completes the statement or answers the question. -If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x) = 17 - . How many candy bars must be sold to maximize revenue?

For the given expression , find y'' and sketch the general shape of the graph of y = f(x). - = (x - 5)

Find an antiderivative of the given function. -24 - 16x - 8

Express the relationship between a small change in x and the corresponding change in y in the form . -y = csc( 5 - 1)

Solve the problem. -From a thin piece of cardboard 50 in. by 50 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

Provide an appropriate response. -Suppose the velocity of a body moving along the s-axis is = 9.8t - 6. Is it necessary to know the initial position of the body to find the body's displacement over some time interval? Justify your answer.

Write the word or phrase that best completes each statement or answers the question. -Sketch a continuous curve y = f(x) with the following properties: f(2) = 3; (x) > 0 for x > 4; and (x) < 0 for x < 4 .

Find the largest open interval where the function is changing as requested. -Decreasing f(x) = -

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = csc x - 2x on [0, 4]

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 4: Applications of the Derivative

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Find an antiderivative of the given function. -

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = 2x3 - 15x2 + 24x

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Find the most general antiderivative. - dx

Express the relationship between a small change in x and the corresponding change in y in the form . -y = 3 -

Use Newton's method to find an approximate answer to the question. Round to six decimal places. -Where are the inflection points of f(x) = + - 5 + 3 located?

Find an antiderivative of the given function. -9 cos 8x

Find the value or values of c that satisfy the equation = (c) in the conclusion of the Mean Value Theorem for the function and interval. -f(x) = x, [-1, 1]

Choose the one alternative that best completes the statement or answers the question. -The graph below shows the first derivative of a function y = f(x). Select a possible graph of f that passes through the point P.

Use differentiation to determine whether the integral formula is correct. -

Choose the one alternative that best completes the statement or answers the question. -If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x) = 17 - . How many candy bars must be sold to maximize revenue?

For the given expression , find y'' and sketch the general shape of the graph of y = f(x). - = (x - 5)

Find an antiderivative of the given function. -24 - 16x - 8

Express the relationship between a small change in x and the corresponding change in y in the form . -y = csc( 5 - 1)

Solve the problem. -From a thin piece of cardboard 50 in. by 50 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

Provide an appropriate response. -Suppose the velocity of a body moving along the s-axis is = 9.8t - 6. Is it necessary to know the initial position of the body to find the body's displacement over some time interval? Justify your answer.

Write the word or phrase that best completes each statement or answers the question. -Sketch a continuous curve y = f(x) with the following properties: f(2) = 3; (x) > 0 for x > 4; and (x) < 0 for x < 4 .

Find the largest open interval where the function is changing as requested. -Decreasing f(x) = -

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = csc x - 2x on [0, 4]

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = 2x³ - 15x² + 24x