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Let = arctan(a) So X I = (a) Find the Taylor polynomial of order 2, P2(x), about x arctan(2). (b) Use Lagrange's formula for the remainder R₂(x) V 0 arctan(r) X -dx dx. (c) Hence calculate I with an error up to 9' = = 0 for the function arctan(x) - P₂(x) to show that · S² P₁(x) dx | ≤ 1/1/ X 9

Let = arctan(a) So X I = (a) Find the Taylor polynomial of order 2, P2(x), about x arctan(2). (b) Use Lagrange's formula for the remainder R₂(x) V 0 arctan(r) X -dx dx. (c) Hence calculate I with an error up to 9' = = 0 for the function arctan(x) - P₂(x) to show that · S² P₁(x) dx | ≤ 1/1/ X 9

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi! I am stuck with part b) of my calculus of one variable homework question (attached). 

I have found a) wherein P2(x) = x

For b) I have found that R2(x) = [x^3(3c^2-1)]/[3(c^2+1)^2]

Other than that I am stuck :(

 

Let = (₁² S I = V 0 arctan(x) X (a) Find the Taylor polynomial of order 2, P2(x), about x = 0 for the function arctan(x). dx. (b) Use Lagrange's formula for the remainder R₂(x): (c) Hence calculate I with an error up to 1. = arctan(x) - P₂(x) to show that arctan(x) dx - [² P² (²) dr | ≤ = S 1 P₂(x) 1 -dx X X 0
Transcribed Image Text:Let = (₁² S I = V 0 arctan(x) X (a) Find the Taylor polynomial of order 2, P2(x), about x = 0 for the function arctan(x). dx. (b) Use Lagrange's formula for the remainder R₂(x): (c) Hence calculate I with an error up to 1. = arctan(x) - P₂(x) to show that arctan(x) dx - [² P² (²) dr | ≤ = S 1 P₂(x) 1 -dx X X 0
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