Question 1

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Accepted Answer

A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent 
A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent

Question 2

Imagine a ball dropped from a height of 40 meters. Each time it strikes the ground, it bounces 0.68 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

Accepted Answer

A)  27.2 meters 
B)  0.32 meters 
C)  210 meters 
D)  40 meters 
A)  27.2 meters 
B)  0.32 meters 
C)  210 meters 
D)  40 meters

Question 3

Use the even/odd properties of   to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.

Accepted Answer

A)  The Fourier Series will contain only cosine terms. 
B)  The Fourier Series will contain only sine terms. 
C)  The Fourier Series will contain both cosine and sine terms. 
A)  The Fourier Series will contain only cosine terms. 
B)  The Fourier Series will contain only sine terms. 
C)  The Fourier Series will contain both cosine and sine terms.

Question 4

Determine if   is absolutely convergent, conditionally convergent or divergent.

Accepted Answer

A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent 
A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent

Question 5

Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.

Accepted Answer

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

Question 6

Evaluate the limit.

Accepted Answer

A)  10 
B)  0 
C)  1 
D)  limit does not exist 
A)  10 
B)  0 
C)  1 
D)  limit does not exist

Question 7

Determine if   converges or diverges. Show your work.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& so @#IMG-DLM& for all @#IMG-DLM& . Thu

Question 8

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Accepted Answer

A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent 
A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent

Question 9

Determine if   is absolutely convergent, conditionally convergent or divergent.

Accepted Answer

A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent 
A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent

Question 10

Use a known Taylor series to find the Taylor series about c = 0 for   , and find its radius of convergence.

Accepted Answer

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

Question 11

Find a power series representation and radius of convergence for   by integrating or differentiating a series.

Accepted Answer

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

Question 12

Use a Taylor polynomial for of degree 3 for the function   to approximate   about c = 1.

Accepted Answer

A)  1.0317 
B)  1.0440 
C)  1.0563 
D)  1.0631 
A)  1.0317 
B)  1.0440 
C)  1.0563 
D)  1.0631

Question 13

Find the MacLaurin series and its interval of convergence.

Accepted Answer

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

Question 14

Find the MacLaurin series and its interval of convergence.

Accepted Answer

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

Question 15

Determine whether the sequence converges or diverges.

Accepted Answer

A)  converges to 0 
B)  converges to 1 
C)  converges to   
D)  diverges 
A)  converges to 0 
B)  converges to 1 
C)  converges to   
D)  diverges

Question 16

Use the even/odd properties of   to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.

Accepted Answer

A)  The Fourier Series will contain only cosine terms. 
B)  The Fourier Series will contain only sine terms. 
C)  The Fourier Series will contain both cosine and sine terms. 
A)  The Fourier Series will contain only cosine terms. 
B)  The Fourier Series will contain only sine terms. 
C)  The Fourier Series will contain both cosine and sine terms.

Question 17

Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .

Accepted Answer

A)  converges with sum =   
B)  converges with sum =   
C)  converges with sum =   
D)  diverges 
A)  converges with sum =   
B)  converges with sum =   
C)  converges with sum =   
D)  diverges

Question 18

Find the Fourier Series of   on the interval   .

Accepted Answer

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

Question 19

Find the Taylor series about c = 5 and its interval of convergence.

Accepted Answer

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

Question 20

Find the Fourier Series of   on the interval   .

Accepted Answer

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

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Imagine a ball dropped from a height of 40 meters. Each time it strikes the ground, it bounces 0.68 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

Use the even/odd properties of to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.

Determine if is absolutely convergent, conditionally convergent or divergent.

Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.

Evaluate the limit.

Determine if converges or diverges. Show your work.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Determine if is absolutely convergent, conditionally convergent or divergent.

Use a known Taylor series to find the Taylor series about c = 0 for , and find its radius of convergence.

Find a power series representation and radius of convergence for by integrating or differentiating a series.

Use a Taylor polynomial for of degree 3 for the function to approximate about c = 1.

Find the MacLaurin series and its interval of convergence.

Find the MacLaurin series and its interval of convergence.

Determine whether the sequence converges or diverges.

Use the even/odd properties of to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.

Use graphical and numerical evidence to conjecture whether the series converges or diverges. .

Find the Fourier Series of on the interval .

Find the Taylor series about c = 5 and its interval of convergence.

Find the Fourier Series of on the interval .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

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 10: Infinite Series

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Imagine a ball dropped from a height of 40 meters. Each time it strikes the ground, it bounces 0.68 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

Use the even/odd properties of to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.

Determine if is absolutely convergent, conditionally convergent or divergent.

Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.

Evaluate the limit.

Determine if converges or diverges. Show your work.

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Determine if is absolutely convergent, conditionally convergent or divergent.

Use a known Taylor series to find the Taylor series about c = 0 for , and find its radius of convergence.

Find a power series representation and radius of convergence for by integrating or differentiating a series.

Use a Taylor polynomial for of degree 3 for the function to approximate about c = 1.

Find the MacLaurin series and its interval of convergence.

Find the MacLaurin series and its interval of convergence.

Determine whether the sequence converges or diverges.

Use the even/odd properties of to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.

Use graphical and numerical evidence to conjecture whether the series converges or diverges. .

Find the Fourier Series of on the interval .

Find the Taylor series about c = 5 and its interval of convergence.

Find the Fourier Series of on the interval .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

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