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 convergence or divergence of the series.

Accepted Answer

Since   and the series   is a convergent p-series, the given series converges by the Limit Comparison Test.

Question 3

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

Accepted Answer

Answers may vary.
Let   . Since   for all   , and since   is decreasing and non-zero for all   , then we can use the Error Estimate Theorem for the Integral Test.

Question 4

Use a known Taylor polynomial with 3 non-zero terms to estimate the value of   .

Accepted Answer

A)  1.8922 
B)  3.7844 
C)  0 
D)    
A)  1.8922 
B)  3.7844 
C)  0 
D)

Question 5

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

Accepted Answer

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

Question 6

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 7

Find the Taylor series about c = 1 and its interval of convergence.

Accepted Answer

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

Question 8

Write a formula that produces the given terms of the sequence.     ,   ,

Accepted Answer

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

Question 9

Suppose that the total salary of all the employees at a factory in a certain city is $350,000. Of this salary, 80% is spent in the city. Of the money spent in the city, 80% is again spent in the city. If this continues indefinitely, how much total money is spent in the city, that is, how much of an effect does the original total salary have on the local economy?

Accepted Answer

A)  $2,800,000 
B)  $504,000 
C)  $1,400,000 
D)  $683,200 
A)  $2,800,000 
B)  $504,000 
C)  $1,400,000 
D)  $683,200

Question 10

Determine how many terms are needed to estimate   to within 0.001.

Accepted Answer

A)  k = 8000 
B)  k = 13 
C)  k = 89 
D)  k = 5 
A)  k = 8000 
B)  k = 13 
C)  k = 89 
D)  k = 5

Question 11

Find the Fourier Series of   on the interval   .

Accepted Answer

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

Question 12

Determine whether the series is convergent or divergent.

Accepted Answer

Since @#IMG-DLM& the

Question 13

Determine whether the series is convergent or divergent.

Accepted Answer

We have that @#IMG-DLM& .
To show @#IMG-DLM& note

Question 14

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 15

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 16

Use a known Taylor series to conjecture the value of   .

Accepted Answer

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

Question 17

Find the limit of the sequence   .

Accepted Answer

A)  0 
B)  8 
C)    
D)  does not exist 
A)  0 
B)  8 
C)    
D)  does not exist

Question 18

Graph   about c =   and the Taylor polynomials for n = 3 and n = 6.

Accepted Answer

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

Question 19

Determine the radius and interval of convergence.

Accepted Answer

A)      
B)      
C)      
D)    converges for   
A)      
B)      
C)      
D)    converges for

Question 20

Prove that   converges to   by showing that   . Show all your work.

Accepted Answer

The answer of Prove that   converges to ...

Determine all values of c such that the series converges.

Determine convergence or divergence of the series.

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

Use a known Taylor polynomial with 3 non-zero terms to estimate the value of .

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

Determine if is absolutely convergent, conditionally convergent or divergent.

Find the Taylor series about c = 1 and its interval of convergence.

Write a formula that produces the given terms of the sequence. , ,

Determine how many terms are needed to estimate to within 0.001.

Find the Fourier Series of on the interval .

Determine whether the series is convergent or divergent.

Determine whether the series is convergent or divergent.

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

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

Use a known Taylor series to conjecture the value of .

Find the limit of the sequence .

Graph about c = and the Taylor polynomials for n = 3 and n = 6.

Determine the radius and interval of convergence.

Prove that converges to by showing that . Show all your work.

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 all values of c such that the series converges.

Determine convergence or divergence of the series.

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

Use a known Taylor polynomial with 3 non-zero terms to estimate the value of .

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

Determine if is absolutely convergent, conditionally convergent or divergent.

Find the Taylor series about c = 1 and its interval of convergence.

Write a formula that produces the given terms of the sequence. , ,

Determine how many terms are needed to estimate to within 0.001.

Find the Fourier Series of on the interval .

Determine whether the series is convergent or divergent.

Determine whether the series is convergent or divergent.

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

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

Use a known Taylor series to conjecture the value of .

Find the limit of the sequence .

Graph about c = and the Taylor polynomials for n = 3 and n = 6.

Determine the radius and interval of convergence.

Prove that converges to by showing that . Show all your work.

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