Question 1

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

Accepted Answer

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

Question 2

Suppose that the probability that a person will remember between 100a% and 100b% of material learned in an experiment is   where x represents the proportion remembered. Determine from the figure below, the probability that a randomly chosen individual will recall between 40% and 65% of the material? Express your answer as a percent rounded to three decimal places. ​   ​

Accepted Answer

A)  23.600% 
B)  7.700% 
C)  14.300% 
D)  33.500% 
E)  119.700% 
A)  23.600% 
B)  7.700% 
C)  14.300% 
D)  33.500% 
E)  119.700%

Question 3

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 4

Find the derivative of the function   . ​

Accepted Answer

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

Question 5

Solve the differential equation. ​   ​

Accepted Answer

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

Question 6

Find the indefinite integral   . ​

Accepted Answer

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

Question 7

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​   ​

Accepted Answer

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

Question 8

Write the limit   , as a definite integral on the interval [0, 4] where   is any point in the   subinterval. ​

Accepted Answer

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

Question 9

Evaluate the following definite integral. ​   ​
Use a graphing utility to check your answer.
​

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Evaluate the function   . If the value is not a rational number, give the answer to three-decimal-place accuracy.

Accepted Answer

A)  15.049 
B)  2.418 
C)  7.254 
D)  3.627 
E)  2.508 
A)  15.049 
B)  2.418 
C)  7.254 
D)  3.627 
E)  2.508

Question 14

Find the indefinite integral   . ​

Accepted Answer

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

Question 15

Find the limit of   as   . ​   ​

Accepted Answer

A)  0 
B)  unbounded 
C)  1/4 
D)  3/2 
E)  3/4 
A)  0 
B)  unbounded 
C)  1/4 
D)  3/2 
E)  3/4

Question 16

Find the general solution of the differential equation below and check the result by differentiation. ​   ​

Accepted Answer

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

Question 17

Find the indefinite integral   . ​

Accepted Answer

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

Question 18

Evaluate   . ​

Accepted Answer

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

Question 19

The graph of the function   is given below. Which of the following definite integrals yields the area of the shaded region? ​   ​

Accepted Answer

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

Question 20

Use integration to find the particular solution of the differential equation   which passes through the point   .

Accepted Answer

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

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

Find the indefinite integral.

Find the derivative of the function .

Solve the differential equation.

Find the indefinite integral .

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Write the limit , as a definite integral on the interval [0, 4] where is any point in the subinterval.

Evaluate the following definite integral. Use a graphing utility to check your answer.

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

Find the indefinite integral.

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

Evaluate the function . If the value is not a rational number, give the answer to three-decimal-place accuracy.

Find the indefinite integral .

Find the limit of as .

Find the general solution of the differential equation below and check the result by differentiation.

Find the indefinite integral .

Evaluate .

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

Use integration to find the particular solution of the differential equation which passes through the point .

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

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

Find the indefinite integral. ​ ​

Find the derivative of the function . ​

Solve the differential equation. ​ ​

Find the indefinite integral . ​

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​ ​

Write the limit , as a definite integral on the interval [0, 4] where is any point in the subinterval. ​

Evaluate the following definite integral. ​ ​ Use a graphing utility to check your answer. ​

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

Find the indefinite integral. ​ ​

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

Evaluate the function . If the value is not a rational number, give the answer to three-decimal-place accuracy.

Find the indefinite integral . ​

Find the limit of as . ​ ​

Find the general solution of the differential equation below and check the result by differentiation. ​ ​

Find the indefinite integral . ​

Evaluate . ​

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region? ​ ​

Use integration to find the particular solution of the differential equation which passes through the point .

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

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

Find the indefinite integral.

Find the derivative of the function .

Solve the differential equation.

Find the indefinite integral .

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Write the limit , as a definite integral on the interval [0, 4] where is any point in the subinterval.

Evaluate the following definite integral. Use a graphing utility to check your answer.

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

Find the indefinite integral.

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

Find the indefinite integral .

Find the limit of as .

Find the general solution of the differential equation below and check the result by differentiation.

Find the indefinite integral .

Evaluate .

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?