Question 1

Find the median (another measure of average) for a random variable with pdf   on   The median is the 50% mark on probability, that is, the value   such that

Accepted Answer

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

Question 2

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is   , what fraction of the molecules will have a molecular weight between 5,000 and 10,000? Round your answer to three decimal places.

Accepted Answer

A)  0.993 
B)  0.280 
C)  0.287 
D)  0.529 
A)  0.993 
B)  0.280 
C)  0.287 
D)  0.529

Question 3

Find an antiderivative.

Accepted Answer

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

Question 4

Evaluate the integral.

Accepted Answer

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

Question 5

Use a comparison to determine whether the integral converges or diverges.

Accepted Answer

A)  The integral converges. 
B)  The integral diverges. 
A)  The integral converges. 
B)  The integral diverges.

Question 6

Find the median of x, rounded to three decimal places, given the pdf   ,   . [Hint: Do not waste time trying to find an analytic solution. Once you determine the expression you would like to solve, just identify which of the choices is close to the correct answer.]

Accepted Answer

A)  3.000 
B)  0.420 
C)  0.559 
D)  6.713 
A)  3.000 
B)  0.420 
C)  0.559 
D)  6.713

Question 7

Use a comparison to determine whether the integral converges or diverges.

Accepted Answer

A)  The integral converges. 
B)  The integral diverges. 
A)  The integral converges. 
B)  The integral diverges.

Question 8

Use a table of integrals to find an antiderivative.

Accepted Answer

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

Question 9

Find the partial fraction decomposition.

Accepted Answer

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

Question 10

Is the function   a probability density function on the interval   ?

Accepted Answer

A)  Yes 
B)  No, because the integrated probablility is not 1 
C)  No, because the function can be negative in the range 
A)  Yes 
B)  No, because the integrated probablility is not 1 
C)  No, because the function can be negative in the range

Question 11

Find the value of c which will make the function   a pdf on the interval   .

Accepted Answer

A)  none, since the cosine can be positive or negative 
B)    
C)    
D)    
A)  none, since the cosine can be positive or negative 
B)    
C)    
D)

Question 12

Find the partial fraction decomposition.

Accepted Answer

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

Question 13

Evaluate the integral using integration by parts and substitution.

Accepted Answer

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

Question 14

Evaluate the integral.

Accepted Answer

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

Question 15

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is   , what fraction of the molecules will have a molecular weight less than 500? Round your answer to three decimal places.

Accepted Answer

A)  0.118 
B)  0.882 
C)  0.221 
D)  0.000 
A)  0.118 
B)  0.882 
C)  0.221 
D)  0.000

Question 16

Find the indicated limit.

Accepted Answer

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

Question 17

Use a table of integrals to find an antiderivative.

Accepted Answer

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

Question 18

Evaluate the integral.

Accepted Answer

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

Question 19

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Accepted Answer

A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   . 
A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   .

Question 20

Find   where

Accepted Answer

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

Find the median (another measure of average) for a random variable with pdf on The median is the 50% mark on probability, that is, the value such that

Find an antiderivative.

Evaluate the integral.

Use a comparison to determine whether the integral converges or diverges.

Find the median of x, rounded to three decimal places, given the pdf , . [Hint: Do not waste time trying to find an analytic solution. Once you determine the expression you would like to solve, just identify which of the choices is close to the correct answer.]

Use a comparison to determine whether the integral converges or diverges.

Use a table of integrals to find an antiderivative.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Is the function a probability density function on the interval ?

Find the value of c which will make the function a pdf on the interval .

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Evaluate the integral using integration by parts and substitution.

Evaluate the integral.

Find the indicated limit.

Use a table of integrals to find an antiderivative.

Evaluate the integral.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Find where

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 8: Integration Techniques

Find the median (another measure of average) for a random variable with pdf on The median is the 50% mark on probability, that is, the value such that

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is , what fraction of the molecules will have a molecular weight between 5,000 and 10,000? Round your answer to three decimal places.

Find an antiderivative.

Evaluate the integral.

Use a comparison to determine whether the integral converges or diverges.

Find the median of x, rounded to three decimal places, given the pdf , . [Hint: Do not waste time trying to find an analytic solution. Once you determine the expression you would like to solve, just identify which of the choices is close to the correct answer.]

Use a comparison to determine whether the integral converges or diverges.

Use a table of integrals to find an antiderivative.

Find the partial fraction decomposition.

Is the function a probability density function on the interval ?

Find the value of c which will make the function a pdf on the interval .

Find the partial fraction decomposition.

Evaluate the integral using integration by parts and substitution.

Evaluate the integral.

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is , what fraction of the molecules will have a molecular weight less than 500? Round your answer to three decimal places.

Find the indicated limit.

Use a table of integrals to find an antiderivative.

Evaluate the integral.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Find where

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$