Question 1

Determine all values of c such that the series converges.

Accepted Answer

A)    any real number 
B)  c in the interval   
C)  c in the interval   
D)  c in the interval   
A)    any real number 
B)  c in the interval   
C)  c in the interval   
D)  c in the interval   C

Question 2

Determine whether   converges or diverges. Show all your work.

Accepted Answer

; the limit exists, so the sequence converges.

Question 3

Find the Fourier Series of   on the interval   .

Accepted Answer

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

Question 4

Find the Taylor series about c = 4 and its interval of convergence.

Accepted Answer

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

Question 5

Find a power series representation of   about   Determine the interval of convergence for the power series.

Accepted Answer

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

Question 6

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 7

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 8

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 9

Use a known Taylor series to conjecture the value of   .

Accepted Answer

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

Question 10

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 11

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 12

Estimate the error in the approximation of   as a Taylor polynomial of degree 3 about c = 1. Show all your work.

Accepted Answer

The answer of Estimate the error in the approximation of...

Question 13

Evaluate the limit.

Accepted Answer

A)  9 
B)  0 
C)  1 
D)  limit does not exist 
A)  9 
B)  0 
C)  1 
D)  limit does not exist

Question 14

Estimate the sum of   to within 0.01.

Accepted Answer

A)  2.58 
B)  2.50 
C)  2.53 
D)  -0.17 
A)  2.58 
B)  2.50 
C)  2.53 
D)  -0.17

Question 15

Estimate the error in using   to approximate the sum of   . Show all your work.

Accepted Answer

Answers may vary.
Let @#IMG-DLM& . Since

Question 16

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 17

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 18

For   , estimate the number of terms needed in a Taylor polynomial with c = 1 to guarantee an accuracy of   . Show all your work.

Accepted Answer

Use the Ta

Question 19

Estimate the error in using   to approximate the sum of   . Show all your work.

Accepted Answer

Answers may vary.
Let @#IMG-DLM& . Since

Question 20

Use an appropriate Taylor series to approximate   accurate to within 10-8.

Accepted Answer

A)  3.32011692 
B)  1.22140276 
C)  0.81873075 
D)  1.22314355 
A)  3.32011692 
B)  1.22140276 
C)  0.81873075 
D)  1.22314355

Determine all values of c such that the series converges.

Determine whether converges or diverges. Show all your work.

Find the Fourier Series of on the interval .

Find the Taylor series about c = 4 and its interval of convergence.

Find a power series representation of about Determine the interval of convergence for the power series.

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

Determine whether the series 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.

Use a known Taylor series to conjecture the value of .

Determine if is absolutely convergent, conditionally convergent or divergent.

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

Estimate the error in the approximation of as a Taylor polynomial of degree 3 about c = 1. Show all your work.

Evaluate the limit.

Estimate the sum of to within 0.01.

Estimate the error in using to approximate the sum of . Show all your work.

Determine if is absolutely convergent, conditionally convergent or divergent.

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.

For , estimate the number of terms needed in a Taylor polynomial with c = 1 to guarantee an accuracy of . Show all your work.

Estimate the error in using to approximate the sum of . Show all your work.

Use an appropriate Taylor series to approximate accurate to within 10^-8.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

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 9: Infinite Series

Determine all values of c such that the series converges.

Determine whether converges or diverges. Show all your work.

Find the Fourier Series of on the interval .

Find the Taylor series about c = 4 and its interval of convergence.

Find a power series representation of about Determine the interval of convergence for the power series.

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

Determine whether the series 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.

Use a known Taylor series to conjecture the value of .

Determine if is absolutely convergent, conditionally convergent or divergent.

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

Estimate the error in the approximation of as a Taylor polynomial of degree 3 about c = 1. Show all your work.

Evaluate the limit.

Estimate the sum of to within 0.01.

Estimate the error in using to approximate the sum of . Show all your work.

Determine if is absolutely convergent, conditionally convergent or divergent.

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.

For , estimate the number of terms needed in a Taylor polynomial with c = 1 to guarantee an accuracy of . Show all your work.

Estimate the error in using to approximate the sum of . Show all your work.

Use an appropriate Taylor series to approximate accurate to within 10-8.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

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

Use an appropriate Taylor series to approximate accurate to within 10^-8.