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Problem 11. For this problem you may use the fact that the Taylor series of cos(I) centered at zero is cos(x) = (-1)*,2k (2k)! =1- 2! 10 +... 10! 4! 6! 8! k=0 1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of 2(cos(x)- 1) f(1) = centered at zero. Hint: Start by subtracting 1 from the Taylor series. 2. Use your answer to the previous part to compute the limit: 2(cos(x) – 1) lim

Problem 11. For this problem you may use the fact that the Taylor series of cos(I) centered at zero is cos(x) = (-1)*,2k (2k)! =1- 2! 10 +... 10! 4! 6! 8! k=0 1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of 2(cos(x)- 1) f(1) = centered at zero. Hint: Start by subtracting 1 from the Taylor series. 2. Use your answer to the previous part to compute the limit: 2(cos(x) – 1) lim

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi there please help me with this problem and explain it. It goes together but if you cannot make both please just solve #11 thanks
Problem 10. The power series from the previous problem is the Taylor series for f(a) = e . 00 (-1)*2k x2 = 1- 1! a4 p(x) =E k! 2! k=0 Verify that this is correct by computing the degree 4 Taylor polynomial of f(r) = e- centered at zero. Problem 11. For this problem you may use the fact that the Taylor series of cos(x) centered at zero is (-1)*72k (2k)! g10 +.. 10! cos(r) =1- 2! 6! 8! 4! k=0 1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of 2(cos(z) – 1) f(2) = centered at zero. Hint: Start by subtracting 1 from the Taylor series. 2. Use your answer to the previous part to compute the limit: 2(cos(x) – 1) lim
Transcribed Image Text:Problem 10. The power series from the previous problem is the Taylor series for f(a) = e . 00 (-1)*2k x2 = 1- 1! a4 p(x) =E k! 2! k=0 Verify that this is correct by computing the degree 4 Taylor polynomial of f(r) = e- centered at zero. Problem 11. For this problem you may use the fact that the Taylor series of cos(x) centered at zero is (-1)*72k (2k)! g10 +.. 10! cos(r) =1- 2! 6! 8! 4! k=0 1. Use the Taylor series of cos(x) to find the first 5 nonzero terms in the Taylor series of 2(cos(z) – 1) f(2) = centered at zero. Hint: Start by subtracting 1 from the Taylor series. 2. Use your answer to the previous part to compute the limit: 2(cos(x) – 1) lim
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