Question 1

Find the Maclaurian series for the function   .

Accepted Answer

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

Question 2

Use the Integral Test to determine the convergence or divergence of the series.

Accepted Answer

A)  converges 
B)  diverges 
C)  Integral Test inconclusive 
A)  converges 
B)  diverges 
C)  Integral Test inconclusive

Question 3

Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

Accepted Answer

A)  converges; Integral Test 
B)  converges; Ratio Test 
C)  converges; Alternating Series Test 
D)  diverges; Ratio Test 
E)  diverges; Integral Test 
A)  converges; Integral Test 
B)  converges; Ratio Test 
C)  converges; Alternating Series Test 
D)  diverges; Ratio Test 
E)  diverges; Integral Test

Question 4

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008.

Accepted Answer

A)  6 
B)  4 
C)  5 
D)  8 
E)  3 
A)  6 
B)  4 
C)  5 
D)  8 
E)  3

Question 5

Use the Integral Test to determine the convergence or divergence of the series.

Accepted Answer

A)  diverges 
B)  Integral Test inconclusive 
C)  converges 
A)  diverges 
B)  Integral Test inconclusive 
C)  converges

Question 6

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of f at   . What is P1 called?

Accepted Answer

A)    tangent line to   at   
B)    secant line to   at   
C)    secant line to   at   
D)    secant line to   at   
E)    tangent line to   at   
A)    tangent line to   at   
B)    secant line to   at   
C)    secant line to   at   
D)    secant line to   at   
E)    tangent line to   at

Question 7

Approximate the sum of the series by using the first six terms.

Accepted Answer

A)  5.398 < S < 5.404 
B)  5.393 < S < 5.405 
C)  5.381 < S < 5.416 
D)  5.391 < S < 5.391 
E)  5.297 < S < 5.501 
A)  5.398 < S < 5.404 
B)  5.393 < S < 5.405 
C)  5.381 < S < 5.416 
D)  5.391 < S < 5.391 
E)  5.297 < S < 5.501

Question 8

Use the Direct Comparison Test (if possible) to determine whether the series   converges or diverges.

Accepted Answer

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

Question 9

Match the sequence with its graph.

Accepted Answer

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

Question 10

Find the sum of the convergent series   .

Accepted Answer

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

Question 11

Find the sum of the convergent series.

Accepted Answer

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

Question 12

is the series   converges.

Accepted Answer

A) True 
 B)False

Question 13

Determine the convergence or divergence of the series   using any appropriate test.

Accepted Answer

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

Question 14

Write the first five terms of the sequence of partial sums.

Accepted Answer

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

Question 15

Use the definition to find the Taylor series (centered at c) for the function.

Accepted Answer

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

Question 16

Use the Ratio Test to determine the convergence or divergence of the series   .

Accepted Answer

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

Question 17

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.

Accepted Answer

A)  5 
B)  4 
C)  2 
D)  6 
E)  3 
A)  5 
B)  4 
C)  2 
D)  6 
E)  3

Question 18

Find the values of x for which the series   converges.

Accepted Answer

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

Question 19

Consider the function given by   . Find the interval of convergence for   .

Accepted Answer

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

Question 20

Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.86h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

Accepted Answer

A)  244.57 feet 
B)  441.14 feet 
C)  196.57 feet 
D)  212.57 feet 
E)  228.57 feet 
A)  244.57 feet 
B)  441.14 feet 
C)  196.57 feet 
D)  212.57 feet 
E)  228.57 feet

Find the Maclaurian series for the function .

Use the Integral Test to determine the convergence or divergence of the series.

Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008.

Use the Integral Test to determine the convergence or divergence of the series.

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of f at . What is P₁ called?

Approximate the sum of the series by using the first six terms.

Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.

Match the sequence with its graph.

Find the sum of the convergent series .

Find the sum of the convergent series.

is the series converges.

Determine the convergence or divergence of the series using any appropriate test.

Write the first five terms of the sequence of partial sums.

Use the definition to find the Taylor series (centered at c) for the function.

Use the Ratio Test to determine the convergence or divergence of the series .

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.

Find the values of x for which the series converges.

Consider the function given by . Find the interval of convergence for .

Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.86h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 9: Infinite Series

Find the Maclaurian series for the function .

Use the Integral Test to determine the convergence or divergence of the series.

Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008.

Use the Integral Test to determine the convergence or divergence of the series.

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of f at . What is P1 called?

Approximate the sum of the series by using the first six terms.

Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.

Match the sequence with its graph.

Find the sum of the convergent series .

Find the sum of the convergent series.

is the series converges.

Determine the convergence or divergence of the series using any appropriate test.

Write the first five terms of the sequence of partial sums.

Use the definition to find the Taylor series (centered at c) for the function.

Use the Ratio Test to determine the convergence or divergence of the series .

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.

Find the values of x for which the series converges.

Consider the function given by . Find the interval of convergence for .

Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.86h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of f at . What is P₁ called?