Question 1

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

Accepted Answer

A)    
B) Diverges 
C) 1 
D)    
A)    
B) Diverges 
C) 1 
D)    B

Question 2

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

Accepted Answer

A) divergent 
B) absolutely convergent 
C) conditionally convergent 
A) divergent 
B) absolutely convergent 
C) conditionally convergent B

Question 3

Determine whether the sequence defined by   converges or diverges. If it converges, find its limit.

Accepted Answer

A) 1 
B) Diverges 
C) 0 
D)    
A) 1 
B) Diverges 
C) 0 
D)    C

Question 4

A sequenceis   defined recursively by the equation   for   where   . Use your calculator to guess the limit of the sequence.

Accepted Answer

The answer of A sequenceis   defined recursively by...

Question 5

Find the sum of the series.

Accepted Answer

The answer of Find the sum of the series. ...

Question 6

Find a power series representation for the function and determine the radius of convergence.

Accepted Answer

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

Question 7

Find all positive values of u for which the series   converges.

Accepted Answer

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

Question 8

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.

Accepted Answer

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

Question 9

Find the interval of convergence of the series.

Accepted Answer

A) diverges everywhere 
B)    
C)    
D)    
E)    
A) diverges everywhere 
B)    
C)    
D)    
E)

Question 10

Find the Maclaurin series for   using the definition of a Maclaurin serires.

Accepted Answer

The answer of Find the Maclaurin series for  ...

Question 11

Determine whether the given series is convergent or divergent.

Accepted Answer

The answer of Determine whether the given series is convergent...

Question 12

Use series to approximate the definite integral to within the indicated accuracy.

Accepted Answer

A) 0.1447 
B) 0.0354 
C) 0.0625 
D) 0.0125 
E) 0.2774 
A) 0.1447 
B) 0.0354 
C) 0.0625 
D) 0.0125 
E) 0.2774

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

The answer of Determine whether the given series converges or...

Question 15

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

Accepted Answer

The answer of Use the sum of the first 10...

Question 16

Which of the given series are absolutely convergent?

Accepted Answer

A)    
B)    
A)    
B)

Question 17

Use the Integral Test to determine whether the series is convergent or divergent.

Accepted Answer

The answer of Use the Integral Test to determine whether...

Question 18

Find the radius of convergence and the interval of convergence of the power series.

Accepted Answer

The answer of Find the radius of convergence and the...

Question 19

Express the number   as a ratio of integers.

Accepted Answer

The answer of Express the number   as a...

Question 20

Use the Comparison Test to determine whether the series is convergent or divergent.

Accepted Answer

The answer of Use the Comparison Test to determine whether...

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

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

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.

A sequenceis defined recursively by the equation for where . Use your calculator to guess the limit of the sequence.

Find the sum of the series.

Find a power series representation for the function and determine the radius of convergence.

Find all positive values of u for which the series converges.

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.

Find the interval of convergence of the series.

Find the Maclaurin series for using the definition of a Maclaurin serires.

Determine whether the given series is convergent or divergent.

Use series to approximate the definite integral to within the indicated accuracy.

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

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

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

Which of the given series are absolutely convergent?

Use the Integral Test to determine whether the series is convergent or divergent.

Find the radius of convergence and the interval of convergence of the power series.

Express the number as a ratio of integers.

Use the Comparison Test to determine whether the series is convergent or divergent.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 8: Series

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

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

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.

A sequenceis defined recursively by the equation for where . Use your calculator to guess the limit of the sequence.

Find the sum of the series.

Find a power series representation for the function and determine the radius of convergence.

Find all positive values of u for which the series converges.

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.

Find the interval of convergence of the series.

Find the Maclaurin series for using the definition of a Maclaurin serires.

Determine whether the given series is convergent or divergent.

Use series to approximate the definite integral to within the indicated accuracy.

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

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

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

Which of the given series are absolutely convergent?

Use the Integral Test to determine whether the series is convergent or divergent.

Find the radius of convergence and the interval of convergence of the power series.

Express the number as a ratio of integers.

Use the Comparison Test to determine whether the series is convergent or divergent.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters