Question 1

Determine the interval of convergence and the function to which the power series converges.

Accepted Answer

The answer of Determine the interval of convergence and the...

Question 2

Determine the number of terms needed to obtain the sum of   to within 10-6.

Accepted Answer

A)    or n = 13 
B)    or n = 2 
C)    or n = 4 
D)    or n = -13 
A)    or n = 13 
B)    or n = 2 
C)    or n = 4 
D)    or n = -13

Question 3

Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.

Accepted Answer

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

Question 4

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 5

Use a known Taylor polynomial at c = 0 with 5 non-zero terms to estimate the value of   .

Accepted Answer

A)  0.0786 
B)  0.4433 
C)  3.1031 
D)  0.0633 
A)  0.0786 
B)  0.4433 
C)  3.1031 
D)  0.0633

Question 6

Determine whether the series converges or diverges. If it converges, find its sum.

Accepted Answer

A)  9 
B)    
C)    
D)  diverges 
A)  9 
B)    
C)    
D)  diverges

Question 7

Determine whether the sequence converges or diverges.

Accepted Answer

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

Question 8

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 9

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

Accepted Answer

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

Question 10

Find the Fourier Series of   on the interval   .

Accepted Answer

A)    
B)    
C)    
D)    (the function is already periodic) 
A)    
B)    
C)    
D)    (the function is already periodic)

Question 11

Determine if   converges or diverges. Show your work.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& so by the @#IMG-DLM& - Term

Question 12

Determine all values of p for which the series   converges.

Accepted Answer

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

Question 13

Determine if   converges or diverges. If convergent, find the sum of the series.

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 14

Find the MacLaurin series and its interval of convergence.

Accepted Answer

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

Question 15

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 16

Show that   is bounded. Show all your work.

Accepted Answer

@#IMG-DLM& So, @#IMG-DLM& is b

Question 17

Estimate the sum of   to within 0.01.

Accepted Answer

A)  -0.12 
B)  -0.16 
C)  -0.09 
D)  -0.01 
A)  -0.12 
B)  -0.16 
C)  -0.09 
D)  -0.01

Question 18

Determine the radius and interval of convergence.

Accepted Answer

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

Question 19

Determine convergence or divergence of the series.

Accepted Answer

Since @#IMG-DLM& for all @#IMG-DLM& and

Question 20

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

Determine the interval of convergence and the function to which the power series converges.

Determine the number of terms needed to obtain the sum of to within 10^-6.

Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.

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

Use a known Taylor polynomial at c = 0 with 5 non-zero terms to estimate the value of .

Determine whether the series converges or diverges. If it converges, find its sum.

Determine whether the sequence converges or diverges.

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

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

Find the Fourier Series of on the interval .

Determine if converges or diverges. Show your work.

Determine all values of p for which the series converges.

Determine if converges or diverges. If convergent, find the sum of the series.

Find the MacLaurin series and its interval of convergence.

Determine if is absolutely convergent, conditionally convergent or divergent.

Show that is bounded. Show all your work.

Estimate the sum of to within 0.01.

Determine the radius and interval of convergence.

Determine convergence or divergence of the series.

Determine if is absolutely convergent, conditionally convergent or divergent.

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 the interval of convergence and the function to which the power series converges.

Determine the number of terms needed to obtain the sum of to within 10-6.

Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.

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

Use a known Taylor polynomial at c = 0 with 5 non-zero terms to estimate the value of .

Determine whether the series converges or diverges. If it converges, find its sum.

Determine whether the sequence converges or diverges.

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

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

Find the Fourier Series of on the interval .

Determine if converges or diverges. Show your work.

Determine all values of p for which the series converges.

Determine if converges or diverges. If convergent, find the sum of the series.

Find the MacLaurin series and its interval of convergence.

Determine if is absolutely convergent, conditionally convergent or divergent.

Show that is bounded. Show all your work.

Estimate the sum of to within 0.01.

Determine the radius and interval of convergence.

Determine convergence or divergence of the series.

Determine if is absolutely convergent, conditionally convergent or divergent.

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

Determine the number of terms needed to obtain the sum of to within 10^-6.