Question 1

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

Accepted Answer

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

Question 2

Determine whether the series is convergent or divergent.

Accepted Answer

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

Question 3

Determine whether the series is convergent or divergent.

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find a power series representation for the function.

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error.   Write a such that   .

Accepted Answer

The answer of Use the Alternating Series Estimation Theorem or...

Question 8

Evaluate the indefinite integral as a power series.

Accepted Answer

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

Question 9

Determine whether the sequence convergent or divergent.

Accepted Answer

A) converges 
B) diverges 
A) converges 
B) diverges

Question 10

Determine whether the series converges or diverges.

Accepted Answer

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

Question 11

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 12

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 13

When money is spent on goods and services, those that receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending D dollars. Suppose that each recipient of spent money spends   and saves   of the money that he or she receives. The values c and s are called the marginal propensity to consume and the marginal propensity to save and, of course,   . The number k = 1/s is called the multiplier. What is the multiplier if the marginal propensity to consume is   ?

Accepted Answer

A) 3 
B) 6 
C) 2.5 
D) 7 
E) 4 
A) 3 
B) 6 
C) 2.5 
D) 7 
E) 4

Question 14

Find an approximation of the sum of the series accurate to two decimal places.

Accepted Answer

A) -0.83 
B) -1.02 
C) -0.96 
D) -0.90 
A) -0.83 
B) -1.02 
C) -0.96 
D) -0.90

Question 15

Find the   partial sum   of the telescoping series, and use it to determine whether the series converges or diverges. If it converges, find its sum.

Accepted Answer

The answer of Find the   partial sum ...

Question 16

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

Accepted Answer

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

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

Determine whether the series is convergent or divergent.

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Determine which series is convergent.

Accepted Answer

A)    
B)    
A)    
B)

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

Determine whether the series is convergent or divergent.

Determine whether the series is convergent or divergent.

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

Find a power series representation for the function.

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

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error. Write a such that .

Evaluate the indefinite integral as a power series.

Determine whether the sequence convergent or divergent.

Determine whether the series converges or diverges.

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

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

Find an approximation of the sum of the series accurate to two decimal places.

Find the partial sum of the telescoping series, and use it to determine whether the series converges or diverges. If it converges, find its sum.

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

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

Determine whether the series is convergent or divergent.

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

Determine which series is convergent.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 11: Infinite Sequences and Series

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

Determine whether the series is convergent or divergent.

Determine whether the series is convergent or divergent.

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

Find a power series representation for the function.

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

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error. Write a such that .

Evaluate the indefinite integral as a power series.

Determine whether the sequence convergent or divergent.

Determine whether the series converges or diverges.

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

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

Find an approximation of the sum of the series accurate to two decimal places.

Find the partial sum of the telescoping series, and use it to determine whether the series converges or diverges. If it converges, find its sum.

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

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

Determine whether the series is convergent or divergent.

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

Determine which series is convergent.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters