Can I get some help with writing the proof for question #2? 1. Let f(x) = cos x and n E Ni) Find the Taylor polynomialP2n2nii) Prove that if x E (-1,1], then1|cos x – Pan (x)| <(2n+1)!iii) Find n so large that P2n approximate cos x on [-1, 1] to seven decimal places2. Prove that y1+x < 1+for all x > 0

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Answered: 2. Prove that y1+x < 1+ = for all x > 0…

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2. Prove that y1+x < 1+ = for all x > 0 2

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.2: Remainder And Factor Theorems

Problem 53PS

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Question

Can I get some help with writing the proof for question #2?

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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