Question 1

Find the derivative of the function   . ​

Accepted Answer

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

Question 2

Find the indefinite integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these 
A)    
B)    
C)    
D)    
E)  none of these

Question 3

Find the derivative of the function   . ​

Accepted Answer

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

Question 4

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A)  6,918 
B)  8,646 
C)  17,970 
D)  6,882 
E)  89,676 
A)  6,918 
B)  8,646 
C)  17,970 
D)  6,882 
E)  89,676

Question 5

Evaluate the limit   first by using techniques from Chapter 1 then by using L'Hopital's Rule. ​

Accepted Answer

A)    
B)  0 
C)    
D)    
E)  does not exist 
A)    
B)  0 
C)    
D)    
E)  does not exist

Question 6

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A)  729 
B)  756 
C)  594 
D)  1,458 
E)  216 
A)  729 
B)  756 
C)  594 
D)  1,458 
E)  216

Question 7

Evaluate the definite integral   . ​

Accepted Answer

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

Question 8

Find the area of the region given below bounded by the graph of   . ​   ​

Accepted Answer

A)  6 
B)    
C)    
D)  7 
E)    
A)  6 
B)    
C)    
D)  7 
E)

Question 9

Evaluate the definite integral of the algebraic function. ​   ​
Use a graphing utility to verify your results.
​

Accepted Answer

A)  -125 
B)  -40 
C)  40 
D)  -51 
E)  50 
A)  -125 
B)  -40 
C)  40 
D)  -51 
E)  50

Question 10

Evaluate   and   in that order. ​

Accepted Answer

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

Question 11

Find the indefinite integral   . ​

Accepted Answer

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

Question 12

Find the indefinite integral   . ​

Accepted Answer

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

Question 13

Find the indefinite integral   . ​

Accepted Answer

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

Question 14

Evaluate the limit   using L'Hopital's Rule if necessary. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  0 
A)    
B)    
C)    
D)    
E)  0

Question 15

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A)  972 
B)  756 
C)  783 
D)  1,836 
E)  594 
A)  972 
B)  756 
C)  783 
D)  1,836 
E)  594

Question 16

Use the limit process to find the area of the region between the graph of the function   and x-axis over the interval [-11, 11]. ​

Accepted Answer

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

Question 17

Evaluate   and   in that order. ​

Accepted Answer

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

Question 18

Evaluate the limit   , using L'Hopital's Rule if necessary. ​

Accepted Answer

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

Question 19

Find the integral of   . ​

Accepted Answer

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

Question 20

Evaluate the following definite integral by the limit definition. ​   ​

Accepted Answer

A)  -6,335 
B)    
C)  -6,340 
D)  -1,575 
E)    
A)  -6,335 
B)    
C)  -6,340 
D)  -1,575 
E)

Find the derivative of the function .

Find the indefinite integral .

Find the derivative of the function .

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Evaluate the definite integral .

Find the area of the region given below bounded by the graph of .

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

Evaluate and in that order.

Find the indefinite integral .

Find the indefinite integral .

Find the indefinite integral .

Evaluate the limit using L'Hopital's Rule if necessary.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval [-11, 11].

Evaluate and in that order.

Evaluate the limit , using L'Hopital's Rule if necessary.

Find the integral of .

Evaluate the following definite integral by the limit definition.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 5: Integration

Find the derivative of the function . ​

Find the indefinite integral . ​

Find the derivative of the function . ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule. ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

Evaluate the definite integral . ​

Find the area of the region given below bounded by the graph of . ​ ​

Evaluate the definite integral of the algebraic function. ​ ​ Use a graphing utility to verify your results. ​

Evaluate and in that order. ​

Find the indefinite integral . ​

Find the indefinite integral . ​

Find the indefinite integral . ​

Evaluate the limit using L'Hopital's Rule if necessary. ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval [-11, 11]. ​

Evaluate and in that order. ​

Evaluate the limit , using L'Hopital's Rule if necessary. ​

Find the integral of . ​

Evaluate the following definite integral by the limit definition. ​ ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find the derivative of the function .

Find the indefinite integral .

Find the derivative of the function .

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Evaluate the definite integral .

Find the area of the region given below bounded by the graph of .

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

Evaluate and in that order.

Find the indefinite integral .

Find the indefinite integral .

Find the indefinite integral .

Evaluate the limit using L'Hopital's Rule if necessary.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval [-11, 11].

Evaluate and in that order.

Evaluate the limit , using L'Hopital's Rule if necessary.

Find the integral of .

Evaluate the following definite integral by the limit definition.