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
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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