Question 1

Use a known Taylor series to conjecture the value of   .

Accepted Answer

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

Question 2

Use a known Taylor polynomial at   with 4 non-zero terms to estimate the value of   .

Accepted Answer

A)  0 
B)  0.8334 
C)  0.2084 
D)  0.4167 
A)  0 
B)  0.8334 
C)  0.2084 
D)  0.4167

Question 3

Determine whether the series is convergent or divergent.

Accepted Answer

Since @#IMG-DLM& the

Question 4

Determine all values of p for which the series   converges.

Accepted Answer

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

Question 5

Find the limit of the sequence.

Accepted Answer

A)  1 
B)    
C)  7 
D)  2 
A)  1 
B)    
C)  7 
D)  2

Question 6

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 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

A)  3.00416602 
B)  1.10517092 
C)  0.90483742 
D)  1.10536052 
A)  3.00416602 
B)  1.10517092 
C)  0.90483742 
D)  1.10536052

Question 9

Determine the radius and interval of convergence of   .

Accepted Answer

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

Question 10

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

Accepted Answer

Let @#IMG-DLM& . f(x) is continuous and

Question 11

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

Accepted Answer

The Comparison Test can be use

Question 12

Determine the radius and interval of convergence.

Accepted Answer

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

Question 13

Determine convergence or divergence of the series.

Accepted Answer

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

Question 14

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 15

Determine whether   is increasing, decreasing or neither.

Accepted Answer

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

Question 16

Graph   about c = 1 and the Taylor polynomials for n = 3 and n = 5.

Accepted Answer

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

Question 17

Determine the radius and interval of convergence of   .

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Determine whether   converges or diverges. Show all your work.

Accepted Answer

@#IMG-DLM& ; the limit does no

Question 20

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

Accepted Answer

A)  20 
B)  55 
C)  209 
D)  2,250,001 
A)  20 
B)  55 
C)  209 
D)  2,250,001

Use a known Taylor series to conjecture the value of .

Use a known Taylor polynomial at with 4 non-zero terms to estimate the value of .

Determine whether the series is convergent or divergent.

Determine all values of p for which the series converges.

Find the limit of the sequence.

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

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

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

Determine the radius and interval of convergence of .

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

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

Determine the radius and interval of convergence.

Determine convergence or divergence of the series.

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

Determine whether is increasing, decreasing or neither.

Graph about c = 1 and the Taylor polynomials for n = 3 and n = 5.

Determine the radius and interval of convergence of .

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

Determine whether converges or diverges. Show all your work.

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

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

Use a known Taylor series to conjecture the value of .

Use a known Taylor polynomial at with 4 non-zero terms to estimate the value of .

Determine whether the series is convergent or divergent.

Determine all values of p for which the series converges.

Find the limit of the sequence.

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

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

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

Determine the radius and interval of convergence of .

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

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

Determine the radius and interval of convergence.

Determine convergence or divergence of the series.

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

Determine whether is increasing, decreasing or neither.

Graph about c = 1 and the Taylor polynomials for n = 3 and n = 5.

Determine the radius and interval of convergence of .

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

Determine whether converges or diverges. Show all your work.

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

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.

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