BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Finding the Radius of Convergence In Exercises 49–52, find the radius of convergence of (a) f(x), (b) f ' ( x ) , (c) f " ( x ) , and (d) f ( x ) d x .

f ( x ) = n = 1 ( 1 ) n + 1 ( x 1 ) n n

(a)

To determine

To calculate: The radius of convergence of the power series f(x)=n=1(1)n+1(x1)nn.

Explanation

Given Information:

The provided function is f(x)=n=1(1)n+1(x1)nn.

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 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 R= if the series converges for all x.

Calculation:

Consider the function f(x)=n=1(1)n+1(x1)nn

Apply the ratio test as,

limn|an

(b)

To determine

To calculate: The radius of convergence of f(x) where f(x)=n=1(1)n+1(x1)nn.

(c)

To determine

To calculate: The radius of convergence of f(x) where f(x)=n=1(1)n+1(x1)nn.

(d)

To determine

To calculate: The radius of convergence of f(x)dx where the function f(x)=n=1(1)n+1(x1)nn.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 10 Solutions

Show all chapter solutions add
Sect-10.1 P-6SWUSect-10.1 P-7SWUSect-10.1 P-8SWUSect-10.1 P-1ESect-10.1 P-2ESect-10.1 P-3ESect-10.1 P-4ESect-10.1 P-5ESect-10.1 P-6ESect-10.1 P-7ESect-10.1 P-8ESect-10.1 P-9ESect-10.1 P-10ESect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.1 P-53ESect-10.1 P-54ESect-10.1 P-55ESect-10.1 P-56ESect-10.1 P-57ESect-10.1 P-58ESect-10.1 P-59ESect-10.1 P-60ESect-10.1 P-61ESect-10.1 P-62ESect-10.1 P-63ESect-10.1 P-64ESect-10.1 P-65ESect-10.1 P-66ESect-10.1 P-67ESect-10.1 P-68ESect-10.1 P-69ESect-10.1 P-70ESect-10.1 P-71ESect-10.1 P-72ESect-10.1 P-73ESect-10.1 P-74ESect-10.2 P-1CPSect-10.2 P-2CPSect-10.2 P-3CPSect-10.2 P-4CPSect-10.2 P-5CPSect-10.2 P-6CPSect-10.2 P-7CPSect-10.2 P-8CPSect-10.2 P-1SWUSect-10.2 P-2SWUSect-10.2 P-3SWUSect-10.2 P-4SWUSect-10.2 P-5SWUSect-10.2 P-6SWUSect-10.2 P-7SWUSect-10.2 P-8SWUSect-10.2 P-9SWUSect-10.2 P-10SWUSect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 P-25ESect-10.2 P-26ESect-10.2 P-27ESect-10.2 P-28ESect-10.2 P-29ESect-10.2 P-30ESect-10.2 P-31ESect-10.2 P-32ESect-10.2 P-33ESect-10.2 P-34ESect-10.2 P-35ESect-10.2 P-36ESect-10.2 P-37ESect-10.2 P-38ESect-10.2 P-39ESect-10.2 P-40ESect-10.2 P-41ESect-10.2 P-42ESect-10.2 P-43ESect-10.2 P-44ESect-10.2 P-45ESect-10.2 P-46ESect-10.2 P-47ESect-10.2 P-48ESect-10.2 P-49ESect-10.2 P-50ESect-10.2 P-51ESect-10.2 P-52ESect-10.2 P-53ESect-10.2 P-54ESect-10.2 P-55ESect-10.2 P-56ESect-10.2 P-57ESect-10.2 P-58ESect-10.2 P-59ESect-10.2 P-60ESect-10.2 P-61ESect-10.2 P-62ESect-10.2 P-63ESect-10.2 P-64ESect-10.2 P-65ESect-10.2 P-67ESect-10.2 P-68ESect-10.2 P-69ESect-10.2 P-70ESect-10.2 P-71ESect-10.2 P-72ESect-10.2 P-73ESect-10.2 P-74ESect-10.2 P-75ESect-10.2 P-76ESect-10.3 P-1CPSect-10.3 P-2CPSect-10.3 P-3CPSect-10.3 P-4CPSect-10.3 P-5CPSect-10.3 P-1SWUSect-10.3 P-2SWUSect-10.3 P-3SWUSect-10.3 P-4SWUSect-10.3 P-5SWUSect-10.3 P-6SWUSect-10.3 P-7SWUSect-10.3 P-8SWUSect-10.3 P-9SWUSect-10.3 P-10SWUSect-10.3 P-1ESect-10.3 P-2ESect-10.3 P-3ESect-10.3 P-4ESect-10.3 P-5ESect-10.3 P-6ESect-10.3 P-7ESect-10.3 P-8ESect-10.3 P-9ESect-10.3 P-10ESect-10.3 P-11ESect-10.3 P-12ESect-10.3 P-13ESect-10.3 P-14ESect-10.3 P-15ESect-10.3 P-16ESect-10.3 P-17ESect-10.3 P-18ESect-10.3 P-19ESect-10.3 P-20ESect-10.3 P-21ESect-10.3 P-22ESect-10.3 P-23ESect-10.3 P-24ESect-10.3 P-25ESect-10.3 P-26ESect-10.3 P-27ESect-10.3 P-28ESect-10.3 P-29ESect-10.3 P-30ESect-10.3 P-31ESect-10.3 P-32ESect-10.3 P-33ESect-10.3 P-34ESect-10.3 P-35ESect-10.3 P-36ESect-10.3 P-37ESect-10.3 P-38ESect-10.3 P-39ESect-10.3 P-40ESect-10.3 P-41ESect-10.3 P-42ESect-10.3 P-43ESect-10.3 P-44ESect-10.3 P-45ESect-10.3 P-46ESect-10.3 P-47ESect-10.3 P-48ESect-10.3 P-49ESect-10.3 P-50ESect-10.3 P-51ESect-10.3 P-52ESect-10.3 P-53ESect-10.3 P-54ESect-10.3 P-55ESect-10.3 P-56ESect-10.3 P-57ESect-10.3 P-58ESect-10.3 P-59ESect-10.3 P-60ESect-10.3 P-61ESect-10.3 P-62ESect-10.3 P-63ESect-10.3 P-64ESect-10.3 P-65ESect-10.3 P-66ESect-10.3 P-1QYSect-10.3 P-2QYSect-10.3 P-3QYSect-10.3 P-4QYSect-10.3 P-5QYSect-10.3 P-6QYSect-10.3 P-7QYSect-10.3 P-8QYSect-10.3 P-9QYSect-10.3 P-10QYSect-10.3 P-11QYSect-10.3 P-12QYSect-10.3 P-13QYSect-10.3 P-14QYSect-10.3 P-15QYSect-10.3 P-16QYSect-10.3 P-17QYSect-10.3 P-18QYSect-10.3 P-19QYSect-10.3 P-20QYSect-10.3 P-21QYSect-10.3 P-22QYSect-10.3 P-23QYSect-10.4 P-1CPSect-10.4 P-2CPSect-10.4 P-3CPSect-10.4 P-4CPSect-10.4 P-5CPSect-10.4 P-6CPSect-10.4 P-7CPSect-10.4 P-8CPSect-10.4 P-1SWUSect-10.4 P-2SWUSect-10.4 P-3SWUSect-10.4 P-4SWUSect-10.4 P-5SWUSect-10.4 P-6SWUSect-10.4 P-7SWUSect-10.4 P-8SWUSect-10.4 P-9SWUSect-10.4 P-10SWUSect-10.4 P-1ESect-10.4 P-2ESect-10.4 P-3ESect-10.4 P-4ESect-10.4 P-5ESect-10.4 P-6ESect-10.4 P-7ESect-10.4 P-8ESect-10.4 P-9ESect-10.4 P-10ESect-10.4 P-11ESect-10.4 P-12ESect-10.4 P-13ESect-10.4 P-14ESect-10.4 P-15ESect-10.4 P-16ESect-10.4 P-17ESect-10.4 P-18ESect-10.4 P-19ESect-10.4 P-20ESect-10.4 P-21ESect-10.4 P-22ESect-10.4 P-23ESect-10.4 P-24ESect-10.4 P-25ESect-10.4 P-26ESect-10.4 P-27ESect-10.4 P-28ESect-10.4 P-29ESect-10.4 P-30ESect-10.4 P-31ESect-10.4 P-32ESect-10.4 P-33ESect-10.4 P-34ESect-10.4 P-35ESect-10.4 P-36ESect-10.4 P-37ESect-10.4 P-38ESect-10.4 P-39ESect-10.4 P-40ESect-10.4 P-41ESect-10.4 P-42ESect-10.4 P-43ESect-10.4 P-44ESect-10.4 P-45ESect-10.4 P-46ESect-10.4 P-47ESect-10.4 P-48ESect-10.4 P-49ESect-10.4 P-50ESect-10.4 P-51ESect-10.4 P-52ESect-10.4 P-53ESect-10.4 P-54ESect-10.4 P-55ESect-10.4 P-56ESect-10.4 P-57ESect-10.4 P-58ESect-10.5 P-1CPSect-10.5 P-2CPSect-10.5 P-3CPSect-10.5 P-1SWUSect-10.5 P-2SWUSect-10.5 P-3SWUSect-10.5 P-4SWUSect-10.5 P-5SWUSect-10.5 P-6SWUSect-10.5 P-7SWUSect-10.5 P-8SWUSect-10.5 P-9SWUSect-10.5 P-10SWUSect-10.5 P-1ESect-10.5 P-2ESect-10.5 P-3ESect-10.5 P-4ESect-10.5 P-5ESect-10.5 P-6ESect-10.5 P-7ESect-10.5 P-8ESect-10.5 P-9ESect-10.5 P-10ESect-10.5 P-11ESect-10.5 P-12ESect-10.5 P-13ESect-10.5 P-14ESect-10.5 P-15ESect-10.5 P-16ESect-10.5 P-17ESect-10.5 P-18ESect-10.5 P-19ESect-10.5 P-20ESect-10.5 P-21ESect-10.5 P-22ESect-10.5 P-23ESect-10.5 P-24ESect-10.5 P-25ESect-10.5 P-26ESect-10.5 P-27ESect-10.5 P-28ESect-10.5 P-29ESect-10.5 P-30ESect-10.5 P-31ESect-10.5 P-32ESect-10.5 P-33ESect-10.5 P-34ESect-10.5 P-35ESect-10.5 P-36ESect-10.6 P-1CPSect-10.6 P-2CPSect-10.6 P-3CPSect-10.6 P-1SWUSect-10.6 P-2SWUSect-10.6 P-3SWUSect-10.6 P-4SWUSect-10.6 P-5SWUSect-10.6 P-6SWUSect-10.6 P-7SWUSect-10.6 P-8SWUSect-10.6 P-9SWUSect-10.6 P-10SWUSect-10.6 P-1ESect-10.6 P-2ESect-10.6 P-3ESect-10.6 P-4ESect-10.6 P-5ESect-10.6 P-6ESect-10.6 P-7ESect-10.6 P-8ESect-10.6 P-9ESect-10.6 P-10ESect-10.6 P-11ESect-10.6 P-12ESect-10.6 P-19ESect-10.6 P-20ESect-10.6 P-21ESect-10.6 P-22ESect-10.6 P-23ESect-10.6 P-24ESect-10.6 P-25ESect-10.6 P-26ESect-10.6 P-27ESect-10.6 P-28ESect-10.6 P-29ESect-10.6 P-30ECh-10 P-1RECh-10 P-2RECh-10 P-3RECh-10 P-4RECh-10 P-5RECh-10 P-6RECh-10 P-7RECh-10 P-8RECh-10 P-9RECh-10 P-10RECh-10 P-11RECh-10 P-12RECh-10 P-13RECh-10 P-14RECh-10 P-15RECh-10 P-16RECh-10 P-17RECh-10 P-18RECh-10 P-19RECh-10 P-20RECh-10 P-21RECh-10 P-22RECh-10 P-23RECh-10 P-24RECh-10 P-25RECh-10 P-26RECh-10 P-27RECh-10 P-28RECh-10 P-29RECh-10 P-30RECh-10 P-31RECh-10 P-32RECh-10 P-33RECh-10 P-34RECh-10 P-35RECh-10 P-36RECh-10 P-37RECh-10 P-38RECh-10 P-39RECh-10 P-40RECh-10 P-41RECh-10 P-42RECh-10 P-43RECh-10 P-44RECh-10 P-45RECh-10 P-46RECh-10 P-47RECh-10 P-48RECh-10 P-49RECh-10 P-50RECh-10 P-51RECh-10 P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-59RECh-10 P-60RECh-10 P-61RECh-10 P-62RECh-10 P-63RECh-10 P-64RECh-10 P-65RECh-10 P-66RECh-10 P-67RECh-10 P-68RECh-10 P-69RECh-10 P-70RECh-10 P-71RECh-10 P-72RECh-10 P-73RECh-10 P-74RECh-10 P-75RECh-10 P-76RECh-10 P-77RECh-10 P-78RECh-10 P-79RECh-10 P-80RECh-10 P-81RECh-10 P-82RECh-10 P-83RECh-10 P-84RECh-10 P-85RECh-10 P-86RECh-10 P-87RECh-10 P-88RECh-10 P-89RECh-10 P-90RECh-10 P-91RECh-10 P-92RECh-10 P-93RECh-10 P-94RECh-10 P-95RECh-10 P-96RECh-10 P-97RECh-10 P-98RECh-10 P-99RECh-10 P-100RECh-10 P-101RECh-10 P-102RECh-10 P-103RECh-10 P-104RECh-10 P-105RECh-10 P-106RECh-10 P-107RECh-10 P-108RECh-10 P-109RECh-10 P-110RECh-10 P-111RECh-10 P-112RECh-10 P-113RECh-10 P-114RECh-10 P-115RECh-10 P-116RECh-10 P-117RECh-10 P-118RECh-10 P-119RECh-10 P-120RECh-10 P-1TYSCh-10 P-2TYSCh-10 P-3TYSCh-10 P-4TYSCh-10 P-5TYSCh-10 P-6TYSCh-10 P-7TYSCh-10 P-8TYSCh-10 P-9TYSCh-10 P-10TYSCh-10 P-11TYSCh-10 P-12TYSCh-10 P-13TYSCh-10 P-14TYSCh-10 P-15TYSCh-10 P-16TYSCh-10 P-17TYSCh-10 P-18TYSCh-10 P-19TYSCh-10 P-20TYSCh-10 P-21TYSCh-10 P-22TYSCh-10 P-23TYSCh-10 P-24TYSCh-10 P-25TYSCh-10 P-26TYSCh-10 P-27TYSCh-10 P-28TYS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Powers Evaluate the power, and write the result in the form a + bi. 50. (2i)4

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 2336, find the domain of the function. 29. f(x)=5x

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problems 17-20, indicate whether the two sets are equal. 19.

Mathematical Applications for the Management, Life, and Social Sciences

Find the prime factorization of 54.

Elementary Technical Mathematics