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1. Let f(x) = cos x and n E N i) Find the Taylor polynomialP2n := P0 2n ii) Prove that if x E [-1,1], then 1 | cos r – Pm (x)| < (2n + 1)! iii) Find n so large that P2n approximate cos x on [-1, 1] to seven decimal places 2. Prove that /1 +x <1+ for all x > 0

1. Let f(x) = cos x and n E N i) Find the Taylor polynomialP2n := P0 2n ii) Prove that if x E [-1,1], then 1 | cos r – Pm (x)| < (2n + 1)! iii) Find n so large that P2n approximate cos x on [-1, 1] to seven decimal places 2. Prove that /1 +x <1+ for all 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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1. Let f(x) = cos x and n E N i) Find the Taylor polynomialP2n 2n ii) Prove that if x E (-1,1], then 1 |cos x – Pan (x)| < (2n+1)! iii) Find n so large that P2n approximate cos x on [-1, 1] to seven decimal places 2. Prove that y1+x < 1+ for all x > 0
Transcribed Image Text:1. Let f(x) = cos x and n E N i) Find the Taylor polynomialP2n 2n ii) Prove that if x E (-1,1], then 1 |cos x – Pan (x)| < (2n+1)! iii) Find n so large that P2n approximate cos x on [-1, 1] to seven decimal places 2. Prove that y1+x < 1+ for all x > 0
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