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f(x) = 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv) (x) = f(¹)(x) = = = = = ✔ f(x) = Σ k=0 f(0) ƒ'(0) f"(0) f"" (0) f(iv) (0) = f(v) (0) x²k = = || = = We see that for the odd terms ƒ(2k+1) (0) = and we also see that for the even derivatives ƒ(²k) (0) = Hence the Taylor series for f centered at 0 is given by = ✔

f(x) = 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv) (x) = f(¹)(x) = = = = = ✔ f(x) = Σ k=0 f(0) ƒ'(0) f"(0) f"" (0) f(iv) (0) = f(v) (0) x²k = = || = = We see that for the odd terms ƒ(2k+1) (0) = and we also see that for the even derivatives ƒ(²k) (0) = Hence the Taylor series for f centered at 0 is given by = ✔

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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f(x) = 1 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv) (x) = f(v) (x) = = = = = = We see that for the odd terms f(2k+¹) (0) ∞ f(x) = Σ k=0 f(0) ƒ'(0) f" (0) f"" (0) f(iv) (0) = f(v) (0) x2k || = || = = = and we also see that for the even derivatives f(2k) (0) Hence the Taylor series for f centered at 0 is given by = ► ✔ ► ←
Transcribed Image Text:f(x) = 1 1+x² Compute f(x) f'(x) f"(x) f""(x) f(iv) (x) = f(v) (x) = = = = = = We see that for the odd terms f(2k+¹) (0) ∞ f(x) = Σ k=0 f(0) ƒ'(0) f" (0) f"" (0) f(iv) (0) = f(v) (0) x2k || = || = = = and we also see that for the even derivatives f(2k) (0) Hence the Taylor series for f centered at 0 is given by = ► ✔ ► ←
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