Explanation Result used: Taylor’s inequality : If | f ( n + 1 ) ( x ) | ≤ M for | x − a | ≤ d , then the nth remainder R n ( x ) of the Taylor series satisfies the inequality | R n ( x ) | ≤ M ( n + 1 ) ! | x − a | n + 1 for | x − a | ≤ d . Calculation: Given that | f ( n + 1 ) ( x ) | ≤ M for all | x − a | ≤ d

Study Guide for Stewart's Multivariable Calculus, 8th

8th Edition

ISBN: 9781305271845

Author: Stewart, James

Publisher: Brooks Cole

See similar textbooks

Videos

Question

Chapter 11.10, Problem 8PT

To determine

For which value, the absolute value of the nth remainder of the Taylor series for y=f(x) about a for |x−a|≤d is less than or equal if |f(n+1)(x)|≤M for all |x−a|≤d.

Expert Solution & Answer

Chapter 11 Solutions

Study Guide for Stewart's Multivariable Calculus, 8th

Ch. 11.1 - limnn2+3n2n2+n+1= a) 0 b) 12 c) 1 d)Ch. 11.1 - Prob. 2PT Ch. 11.1 - Prob. 3PT Ch. 11.1 - Sometimes, Always, or Never: If {an} is increasing...Ch. 11.1 - Prob. 5PT Ch. 11.1 - Prob. 6PT Ch. 11.1 - Prob. 7PT Ch. 11.1 - Prob. 8PT Ch. 11.2 - Prob. 1PT Ch. 11.2 - Prob. 2PT

Ch. 11.2 - Prob. 3PT Ch. 11.2 - Prob. 4PT Ch. 11.2 - Prob. 5PT Ch. 11.2 - Prob. 6PT Ch. 11.2 - Prob. 7PT Ch. 11.2 - Prob. 8PT Ch. 11.3 - For what values of p does the series n=11(n2)p...Ch. 11.3 - True or False: If f(x) is continuous and...Ch. 11.3 - Prob. 3PT Ch. 11.3 - Prob. 4PT Ch. 11.3 - Prob. 5PT Ch. 11.3 - Prob. 6PT Ch. 11.4 - Prob. 1PT Ch. 11.4 - Prob. 2PT Ch. 11.4 - True or False: n=1n+n3n2/3+n3/2+1 is a convergent...Ch. 11.4 - Prob. 4PT Ch. 11.4 - Prob. 5PT Ch. 11.5 - Prob. 1PT Ch. 11.5 - Prob. 2PT Ch. 11.5 - Prob. 3PT Ch. 11.5 - Prob. 4PT Ch. 11.6 - Prob. 1PT Ch. 11.6 - Prob. 2PT Ch. 11.6 - Prob. 3PT Ch. 11.6 - Prob. 4PT Ch. 11.6 - Prob. 5PT Ch. 11.6 - Prob. 6PT Ch. 11.7 - Prob. 1PT Ch. 11.7 - Prob. 2PT Ch. 11.7 - Prob. 3PT Ch. 11.7 - Prob. 4PT Ch. 11.7 - Prob. 5PT Ch. 11.7 - Prob. 6PT Ch. 11.8 - Sometimes, Always, or Never: The interval of...Ch. 11.8 - Prob. 2PT Ch. 11.8 - Prob. 3PT Ch. 11.8 - Prob. 4PT Ch. 11.8 - Prob. 5PT Ch. 11.9 - Prob. 1PT Ch. 11.9 - For f(x)=n=0x2nn!, f(x) = a) n=1x2n1n! b)...Ch. 11.9 - Using 11x=n=0xn for |x| 1, x1x2dx= a) n=0x2n2n b)...Ch. 11.9 - Using 11x=n=0xn for |x| 1 and differentiation,...Ch. 11.9 - From 11x=n=0xn for |x| 1 and substituting 4x2 for...Ch. 11.10 - Given the Taylor Series ex=n=0xnn!, a Taylor...Ch. 11.10 - Prob. 2PT Ch. 11.10 - Prob. 3PT Ch. 11.10 - Prob. 4PT Ch. 11.10 - Prob. 5PT Ch. 11.10 - Prob. 6PT Ch. 11.10 - Prob. 7PT Ch. 11.10 - Prob. 8PT Ch. 11.10 - Prob. 9PT Ch. 11.10 - Prob. 10PT Ch. 11.10 - Using a binomial series, the Maclaurin series for...Ch. 11.10 - Prob. 12PT Ch. 11.11 - Prob. 1PT Ch. 11.11 - Prob. 2PT Ch. 11.11 - Prob. 3PT

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

SEE MORE TEXTBOOKS

Power Series; Author: Professor Dave Explains;https://www.youtube.com/watch?v=OxVBT83x8oc;License: Standard YouTube License, CC-BY

Power Series & Intervals of Convergence; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XHoRBh4hQNU;License: Standard YouTube License, CC-BY

For which value, the absolute value of the n th remainder of the Taylor series for y = f ( x ) about a for | x − a | ≤ d is less than or equal if | f ( n + 1 ) ( x ) | ≤ M for all | x − a | ≤ d .

Solution Summary: The author calculates the nth remainder of the Taylor series for y=f(x) about a value less than or equal.

Videos

For which value, the absolute value of the nth remainder of the Taylor series for y=f(x) about a for |x−a|≤d is less than or equal if |f(n+1)(x)|≤M for all |x−a|≤d.

Chapter 11 Solutions