Question 1

Determine how many terms are needed to estimate   to within 0.0001.

Accepted Answer

A)  k = 30 
B)  k = 31 
C)  k = 9 
D)  k = 0.9999 
A)  k = 30 
B)  k = 31 
C)  k = 9 
D)  k = 0.9999

Question 2

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

Accepted Answer

A)  0.99824797 
B)  -0.05913333 
C)  1.00175305 
D)  -0.75500313 
A)  0.99824797 
B)  -0.05913333 
C)  1.00175305 
D)  -0.75500313

Question 3

Use a known Taylor series to conjecture the value of   .

Accepted Answer

A)  7 
B)    
C)  1 
D)    
A)  7 
B)    
C)  1 
D)

Question 4

Write out terms   of the given sequence.

Accepted Answer

The answer of Write out terms   of the...

Question 5

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 6

Determine convergence or divergence of the series.

Accepted Answer

Since @#IMG-DLM& and the series @#IMG-DLM& is a di

Question 7

Estimate the error in the approximation of   as a Taylor polynomial of degree 4 about c = 1. Show all your work.

Accepted Answer

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

Question 8

Use a Taylor Polynomial of degree 3 to approximate   about c = 1.

Accepted Answer

A)  0.3271 
B)  0.2561 
C)  1.1735 
D)  1.3791 
A)  0.3271 
B)  0.2561 
C)  1.1735 
D)  1.3791

Question 9

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

Accepted Answer

A)  diverges 
B)  converges to 0.9 
C)  converges to   
D)  converges to   
A)  diverges 
B)  converges to 0.9 
C)  converges to   
D)  converges to

Question 10

Determine if   converges or diverges. Show your work.

Accepted Answer

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

Question 11

Find the limit of the sequence   .

Accepted Answer

A)  -4 
B)  0 
C)  4 
D)  does not exist 
A)  -4 
B)  0 
C)  4 
D)  does not exist

Question 12

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 13

Determine the radius and interval of convergence of   .

Accepted Answer

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

Question 14

Find the Fourier Series of   on the interval   .

Accepted Answer

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

Question 15

Show that   is bounded. Show all your work.

Accepted Answer

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

Question 16

Find the interval of convergence and function f(x) to which   converges.

Accepted Answer

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

Question 17

Determine whether   converges or diverges. Show all your work.

Accepted Answer

@#IMG-DLM& ; the lim

Question 18

Determine the convergence or divergence of   .
Show all your work.

Accepted Answer

This is a p-series,

Question 19

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 20

Determine whether   is increasing, decreasing or neither.

Accepted Answer

A)  decreasing 
B)  increasing 
C)  neither 
A)  decreasing 
B)  increasing 
C)  neither

Determine how many terms are needed to estimate to within 0.0001.

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

Use a known Taylor series to conjecture the value of .

Write out terms of the given sequence.

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

Determine convergence or divergence of the series.

Estimate the error in the approximation of as a Taylor polynomial of degree 4 about c = 1. Show all your work.

Use a Taylor Polynomial of degree 3 to approximate about c = 1.

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

Determine if converges or diverges. Show your work.

Find the limit of the sequence .

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

Determine the radius and interval of convergence of .

Find the Fourier Series of on the interval .

Show that is bounded. Show all your work.

Find the interval of convergence and function f(x) to which converges.

Determine whether converges or diverges. Show all your work.

Determine the convergence or divergence of . Show all your work.

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

Determine whether is increasing, decreasing or neither.

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 how many terms are needed to estimate to within 0.0001.

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

Use a known Taylor series to conjecture the value of .

Write out terms of the given sequence.

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

Determine convergence or divergence of the series.

Estimate the error in the approximation of as a Taylor polynomial of degree 4 about c = 1. Show all your work.

Use a Taylor Polynomial of degree 3 to approximate about c = 1.

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

Determine if converges or diverges. Show your work.

Find the limit of the sequence .

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

Determine the radius and interval of convergence of .

Find the Fourier Series of on the interval .

Show that is bounded. Show all your work.

Find the interval of convergence and function f(x) to which converges.

Determine whether converges or diverges. Show all your work.

Determine the convergence or divergence of . Show all your work.

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

Determine whether is increasing, decreasing or neither.

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

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