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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 10.4, Problem 22E
Textbook Problem
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Finding the Radius of Convergence In Exercises 5–24, find the radius of convergence of the power series. See Examples 2 and 3.

n = 0 ( 1 ) n x 2 n n !

To determine

To calculate: The radius of convergence of the power series n=0(1)nx2nn!.

Explanation of Solution

Given Information:

The provided power series is, n=0(1)nx2nn!.

Formula used:

Ratio test:

For an infinite series n=1an with nonzero terms.

a) If limn|an+1an|<1 then the series converges.

b) If limn|an+1an|>1 or limn|an+1an|= then the series diverges.

c) If limn|an+1an|=1 then test is inconclusive.

Convergence of a Power Series:

If a power series is centered at a constant c, then either of the following condition is true.

a) The radius of convergence is R=0 if the series converges only at c.

b) The radius of convergence R exist and is a positive real number such that series converges for |xc|<R and diverges for |xc|>R.

c) The radius of convergence is R= if the series converges for all x.

Calculation:

Consider the power series n=0(1)nx2nn!

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Chapter 10 Solutions

Calculus: An Applied Approach (MindTap Course List)
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Ch. 10.1 - In Exercises 5-8, simplify the expression....Ch. 10.1 - In Exercises 5-8, simplify the expression. 3n+1n3Ch. 10.1 - In Exercises 5-8, simplify the expression....Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Writing Terms of a Sequence In Exercises 1-10,...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the Limit of a Sequence In Exercises...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Finding the limit of a Sequence In Exercises 1130,...Ch. 10.1 - Using Graphs to Determine Convergence In Exercises...Ch. 10.1 - Using Graphs to Determine Convergence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Finding a Pattern for a Sequence In Exercises...Ch. 10.1 - Using Arithmetic Sequences In Exercises 4750,...Ch. 10.1 - Using Arithmetic Sequences In Exercises 4750,...Ch. 10.1 - Using Arithmetic Sequences In Exercises 4750,...Ch. 10.1 - Using Arithmetic Sequences In Exercises 4750,...Ch. 10.1 - Using Geometric Sequences In Exercises 51-54,...Ch. 10.1 - Using Geometric Sequences In Exercises 51-54,...Ch. 10.1 - Using Geometric Sequences In Exercises 51-54,...Ch. 10.1 - Using Geometric Sequences In Exercises 51-54,...Ch. 10.1 - Identifying Sequences In Exercises 55-58,...Ch. 10.1 - Identifying Sequences In Exercises 55-58,...Ch. 10.1 - Identifying Sequences In Exercises 55-58,...Ch. 10.1 - Identifying Sequences In Exercises 55-58,...Ch. 10.1 - Finding a Sequence In Exercises 59 and 60, give an...Ch. 10.1 - Finding a Sequence In Exercises 59 and 60, give an...Ch. 10.1 - Compound Interest Consider the sequence {An},...Ch. 10.1 - Compound Interest Consider the sequence {An},...Ch. 10.1 - Individual Retirement Account A deposit of $2000...Ch. 10.1 - Investment A deposit of $100 is made each month in...Ch. 10.1 - Carbon Dioxide The average concentration levels an...Ch. 10.1 - HOW DO YOU SEE IT? 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(Begin with...Ch. 10.2 - Determine the convergence or divergence of the...Ch. 10.2 - Use the properties of infinite series to find the...Ch. 10.2 - In Exercises 3-6, evaluate the expression. a....Ch. 10.2 - Find the 5th, 50th, and 500th partial sums of the...Ch. 10.2 - A deposit of 520 is made every month for 4 years...Ch. 10.2 - Decide whether each series converges or diverges....Ch. 10.2 - Repeat Example 8 when the manufacturer sells 5000...Ch. 10.2 - In Exercises 1 and 2, add the fractions....Ch. 10.2 - In Exercises 1 and 2, add the fractions....Ch. 10.2 - In Exercises 3-6, evaluate the expression....Ch. 10.2 - In Exercises 3-6, evaluate the expression. 3...Ch. 10.2 - In Exercises 3-6, evaluate the expression. 2...Ch. 10.2 - In Exercises 3-6, evaluate the expression. 6.12...Ch. 10.2 - In Exercises 7-10, find the limit. 7.limx3n4n+1Ch. 10.2 - In Exercises 7-10, find the limit. limn5nn2+4Ch. 10.2 - In Exercises 7-10, find the limit. limnn!n!3Ch. 10.2 - In Exercises 7-10, find the limit. limn2n!+14n!1Ch. 10.2 - Using Sigma Notation In Exercises 14, use sigma...Ch. 10.2 - Using Sigma Notation In Exercises 14, use sigma...Ch. 10.2 - Using Sigma Notation In Exercises 14, use sigma...Ch. 10.2 - Using Sigma Notation In Exercises 14, use sigma...Ch. 10.2 - Finding Partial Sums In Exercises 58, find the...Ch. 10.2 - Finding Partial Sums In Exercises 58, find the...Ch. 10.2 - Finding Partial Sums In Exercises 58, find the...Ch. 10.2 - Finding Partial Sums In Exercises 58, find the...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Verifying Divergence In Exercises 918, verify that...Ch. 10.2 - Using Properties of Infinite Series In Exercises...Ch. 10.2 - Using Properties of Infinite Series In Exercises...Ch. 10.2 - Using Properties of Infinite Series In Exercises...Ch. 10.2 - Using Properties of Infinite Series In Exercises...Ch. 10.2 - Finding an nth Partial Sum In Exercises 23-26,...Ch. 10.2 - Finding an nth Partial Sum In Exercises 23-26,...Ch. 10.2 - Finding an nth Partial Sum In Exercises 23-26,...Ch. 10.2 - Finding an nth Partial Sum In Exercises 23-26,...Ch. 10.2 - Finding the Sum of a Geometric Series In Exercises...Ch. 10.2 - Finding the Sum of a Geometric Series In Exercises...Ch. 10.2 - Finding the Sum of a Geometric Series In Exercises...Ch. 10.2 - Finding the Sum of a Geometric Series In Exercises...Ch. 10.2 - Finding the Sum of a Geometric Series In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Determining Convergence or Divergence In Exercises...Ch. 10.2 - Using Geometric Series In Exercises 4750, the...Ch. 10.2 - Using Geometric Series In Exercises 4750, the...Ch. 10.2 - Using Geometric Series In Exercises 4750, the...Ch. 10.2 - Using Geometric Series In Exercises 4750, the...Ch. 10.2 - Annuity A deposit of $100 is made at the beginning...Ch. 10.2 - Annuity A deposit of $150 is made at the beginning...Ch. 10.2 - Annuity A deposit of P dollars is made every month...Ch. 10.2 - HOW DO YOU SEE IT? The graph shows the revenues...Ch. 10.2 - Sales A company produces a new product for which...Ch. 10.2 - Sales Repeat Exercise 55 with the assumption that...Ch. 10.2 - Physical Science A ball is dropped from a height...Ch. 10.2 - Physical Science A ball is dropped from a height...Ch. 10.2 - Consumer Trends: Multiplier Effect The annual...Ch. 10.2 - Consumer Trends: Multiplier Effect Repeat Exercise...Ch. 10.2 - Depreciation A company buys a machine for $225.000...Ch. 10.2 - Depreciation A company buys a machine for $225.000...Ch. 10.2 - Salary You accept a job that pays a salary of...Ch. 10.2 - Salary You go to work at a company that pays $0.01...Ch. 10.2 - Probability: Coin Toss A fair coin is tossed until...Ch. 10.2 - Probability In Exercises 67 and 68, the random...Ch. 10.2 - Probability In Exercises 67 and 68, the random...Ch. 10.2 - Environment A factory is polluting a river such...Ch. 10.2 - Finance: Annuity The simplest kind of annuity is a...Ch. 10.2 - Finding Sums In Exercises 71-74, use a symbolic...Ch. 10.2 - Finding Sums In Exercises 71-74, use a symbolic...Ch. 10.2 - Finding Sums In Exercises 71-74, use a symbolic...Ch. 10.2 - Finding Sums In Exercises 71-74, use a symbolic...Ch. 10.2 - True or False? 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The graphs show the sequences...Ch. 10.3 - In Exercises 14, write the first five terms of the...Ch. 10.3 - In Exercises 14, write the first five terms of the...Ch. 10.3 - In Exercises 14, write the first five terms of the...Ch. 10.3 - In Exercises 14, write the first five terms of the...Ch. 10.3 - In Exercises 58, find the limit of the sequence...Ch. 10.3 - In Exercises 58, find the limit of the sequence...Ch. 10.3 - In Exercises 5-8, find the limit of the sequence...Ch. 10.3 - In Exercises 58, find the limit of the sequence...Ch. 10.3 - In Exercises 911, write an expression for the nth...Ch. 10.3 - In Exercises 911, write an expression for the nth...Ch. 10.3 - In Exercises 911, write an expression for the nth...Ch. 10.3 - In Exercises 12 and 13, find the sequence of...Ch. 10.3 - In Exercises 12 and 13, find the sequence of...Ch. 10.3 - Find the third, fifth, and seventh partial sums of...Ch. 10.3 - In Exercises 15 and 16, find the sum of the...Ch. 10.3 - In Exercises 15 and 16, find the sum of the...Ch. 10.3 - In Exercises 1722, determine the convergence or...Ch. 10.3 - In Exercises 1722, determine the convergence or...Ch. 10.3 - In Exercises 1722, determine the convergence or...Ch. 10.3 - In Exercises 1722, determine the convergence or...Ch. 10.3 - In Exercises 1722, determine the convergence or...Ch. 10.3 - In Exercises 1722, determine the convergence or...Ch. 10.3 - A deposit of $200 is made at the beginning of each...Ch. 10.4 - Checkpoint 1 Worked-out solution available at...Ch. 10.4 - Checkpoint 2 Worked-out solution available at...Ch. 10.4 - Checkpoint 3 Worked-out solution available at...Ch. 10.4 - Checkpoint 4 Worked-out solution available at...Ch. 10.4 - Checkpoint 5 Worked-out solution available at...Ch. 10.4 - Use the Maclaurin series for ex g(x)=e2x...Ch. 10.4 - Checkpoint 5 Worked-out solution available at...Ch. 10.4 - Checkpoint 5 Worked-out solution available at...Ch. 10.4 - In Exercises 1-4, find f(g(x)) and g(f(x))....Ch. 10.4 - In Exercises 1-4, find f(g(x)) and g(f(x))....Ch. 10.4 - In Exercises 1-4, find f(g(x)) and g(f(x))....Ch. 10.4 - In Exercises 1-4, find f(g(x)) and g(f(x))....Ch. 10.4 - In Exercises 5-8, find f(x),f(x),f(x),andf(4)(x)....Ch. 10.4 - In Exercises 5-8, find f(x),f(x),f(x),andf(4)(x)....Ch. 10.4 - In Exercises 5-8. find f(x),f(x),f(x),andf(4)(x)....Ch. 10.4 - In Exercises 5-8. find f(x),f(x),f(x),andf(4)(x)....Ch. 10.4 - In Exercises 9 and 10, simplify the expression....Ch. 10.4 - In Exercises 9 and 10, simplify the expression....Ch. 10.4 - Using Power Series In Exercises 14, identify the...Ch. 10.4 - Using Power Series In Exercises 14, identify the...Ch. 10.4 - Using Power Series In Exercises 14, identify the...Ch. 10.4 - Using Power Series In Exercises 14, identify the...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding Taylor and Maclaurin Series In Exercises...Ch. 10.4 - Finding a Maclaurin Series In Exercises 33-36, use...Ch. 10.4 - Finding a Maclaurin Series In Exercises 33-36, use...Ch. 10.4 - Finding a Maclaurin Series In Exercises 33-36, use...Ch. 10.4 - Finding a Maclaurin Series In Exercises 33-36, use...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Using the Basic list of Power Series In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding the Radius of Convergence In Exercises...Ch. 10.4 - Finding Power Series In Exercises 5356, find the...Ch. 10.4 - Finding Power Series In Exercises 5356, find the...Ch. 10.4 - Finding Power Series In Exercises 5356, find the...Ch. 10.4 - Finding Power Series In Exercises 5356, find the...Ch. 10.4 - Think About It Consider the geometric series...Ch. 10.4 - HOW DO YOU SEE IT? Match the graph of the first 10...Ch. 10.5 - Find the 12th-degree Taylor polynomial for...Ch. 10.5 - Use the fourth-degree Taylor polynomial from...Ch. 10.5 - Checkpoint 3 Worked-out solution available at...Ch. 10.5 - In Exercises 16, find the power series for the...Ch. 10.5 - In Exercises 16, find the power series for the...Ch. 10.5 - In Exercises 16, find the power series for the...Ch. 10.5 - In Exercises 16, find the power series for the...Ch. 10.5 - In Exercises 16, find the power series for the...Ch. 10.5 - In Exercises 16, find the power series for the...Ch. 10.5 - In Exercises 710, evaluate the definite integral....Ch. 10.5 - In Exercises 710, evaluate the definite integral....Ch. 10.5 - In Exercises 710, evaluate the definite integral....Ch. 10.5 - In Exercises 710, evaluate the definite integral....Ch. 10.5 - Using Taylor Polynomials In Exercises 1 and 2, use...Ch. 10.5 - Using Taylor Polynomials In Exercises 1 and 2, use...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 314, find...Ch. 10.5 - Finding Taylor Polynomials In Exercises 15 and 16,...Ch. 10.5 - Finding Taylor Polynomials In Exercises 15 and 16,...Ch. 10.5 - Finding Taylor Polynomials In Exercises 17 and 18,...Ch. 10.5 - Finding Taylor Polynomials In Exercises 17 and 18,...Ch. 10.5 - Matching In Exercises 19-22, match the Taylor...Ch. 10.5 - Matching In Exercises 19-22, match the Taylor...Ch. 10.5 - Matching In Exercises 19-22, match the Taylor...Ch. 10.5 - Matching In Exercises 19-22, match the Taylor...Ch. 10.5 - Using a Taylor Polynomial Approximation In...Ch. 10.5 - Using a Taylor Polynomial Approximation In...Ch. 10.5 - Using a Taylor Polynomial Approximation In...Ch. 10.5 - Using a Taylor Polynomial Approximation In...Ch. 10.5 - Finding the Maximum Error In Exercises 27 and 28,...Ch. 10.5 - Finding the Maximum Error In Exercises 27 and 28,...Ch. 10.5 - Using the Maximum Error In Exercises 29 and 30,...Ch. 10.5 - Using the Maximum Error In Exercises 29 and 30,...Ch. 10.5 - Approximating a Definite Integral In Exercises...Ch. 10.5 - Approximating a Definite Integral In Exercises...Ch. 10.5 - Approximating a Definite Integral In Exercises...Ch. 10.5 - Approximating a Definite Integral In Exercises...Ch. 10.5 - Comparing Taylor Polynomials Consider the...Ch. 10.5 - HOW DO YOU SEE IT? The graphs show first-,...Ch. 10.6 - Calculate three iterations of Newton's Method to...Ch. 10.6 - Repeat Example 2 for f(x)=x3+2x+1. Use Newtons...Ch. 10.6 - Repeat Example 3 for y=ex2andy=x. 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