Use the sum of the first ten terms to approximate the sum of the series Estimate the error by taking the average of the upper and lower bounds given by Theorem 16. (Hint: Use trigonometric nn2 - 1 n= 2 substitution. Round your answers to three decimal places.) sum 1.822 error

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
Use the sum of the first ten terms to approximate the sum of the series
Estimate the error by taking the average of the upper and lower bounds given by Theorem 16. (Hint: Use trigonometric
ny n2 - 1
n = 2
substitution. Round your answers to three decimal places.)
sum
1.822
error
Transcribed Image Text:Use the sum of the first ten terms to approximate the sum of the series Estimate the error by taking the average of the upper and lower bounds given by Theorem 16. (Hint: Use trigonometric ny n2 - 1 n = 2 substitution. Round your answers to three decimal places.) sum 1.822 error
Theorem 16. Remainder Estimate for the Integral Test
Let f(x) be a positive-valued continuous decreasing function on the interval [1, ∞0) such that
f(n) = a, for every natural number n. If the series a, converges, then
n=1
Lf(x)dx < R, <
J $(x)dx
n+1
Transcribed Image Text:Theorem 16. Remainder Estimate for the Integral Test Let f(x) be a positive-valued continuous decreasing function on the interval [1, ∞0) such that f(n) = a, for every natural number n. If the series a, converges, then n=1 Lf(x)dx < R, < J $(x)dx n+1
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning