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

3. Let I = 0 arctan(2) X (a) Find the Taylor polynomial of order 2, P₂(x), about x = 0 for the function arctan(r). (b) Use Lagrange's formula for the remainder S (c) Hence calculate I with an error up to 1. arctan(x) X -dx. -dx R₂(x) = arctan(x) — P₂(x) to show that P₂(x) dx ≤ 1 So 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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Let I = S. 0 arctan(r) I (a) Find the Taylor polynomial of order 2, P2(x), about x = 0 for the function arctan(r). (b) Use Lagrange's formula for the remainder Sª (c) Hence calculate I with an error up to 3. arctan(r) I -d.x. -dx R₂(x) = arctan(x) - P₂(x) to show that P₂(x) - [² P²(x) dx | ≤ = S x 0

3. Let I = S arctan(r) dư. -dx. X (a) Find the Taylor polynomial of order 2, P2(x), about x = 0 for the function arctan(x). (b) Use Lagrange's formula for the remainder R₂(x) = arctan(x) - P₂(x) to show that 1 1 C - Sổ -dx < 9 arctan(x) X -dx (c) Hence calculate I with an error up to 1. P₂(x) X
Transcribed Image Text:3. Let I = S arctan(r) dư. -dx. X (a) Find the Taylor polynomial of order 2, P2(x), about x = 0 for the function arctan(x). (b) Use Lagrange's formula for the remainder R₂(x) = arctan(x) - P₂(x) to show that 1 1 C - Sổ -dx < 9 arctan(x) X -dx (c) Hence calculate I with an error up to 1. P₂(x) X
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