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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can I get some help with question #1?
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bcaf00b-fd38-43c3-b135-72c037d16fd6%2F965ca91f-dc04-4dc6-859d-706b03e013b1%2Flhkz6nbu_processed.jpeg&w=3840&q=75)
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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