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3. Let arctan(2)dx. -S² x (a) Find the Taylor polynomial of order 2, P₂(x), about x = 0 for the functio arctan(r). (b) Use Lagrange's formula for the remainder R₂(x) = arctan(x) – P₂(x) to show tha (²P₂(2) dx ≤ 1 9 I = arctan(r), -dx x 0

3. Let arctan(2)dx. -S² x (a) Find the Taylor polynomial of order 2, P₂(x), about x = 0 for the functio arctan(r). (b) Use Lagrange's formula for the remainder R₂(x) = arctan(x) – P₂(x) to show tha (²P₂(2) dx ≤ 1 9 I = arctan(r), -dx x 0

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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3. Let =-6² I = arctan(2) X -dx. (a) Find the Taylor polynomial of order 2, P₂(x), about x = 0 for the function arctan(2). (b) Use Lagrange's formula for the remainder R₂(x) = arctan(x) – P₂(x) to show that arctan(2) da P₂(x) S S² -dx X X (c) Hence calculate I with an error up to 3. 1 | ≤ ² 9
Transcribed Image Text:3. Let =-6² I = arctan(2) X -dx. (a) Find the Taylor polynomial of order 2, P₂(x), about x = 0 for the function arctan(2). (b) Use Lagrange's formula for the remainder R₂(x) = arctan(x) – P₂(x) to show that arctan(2) da P₂(x) S S² -dx X X (c) Hence calculate I with an error up to 3. 1 | ≤ ² 9
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