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Let f(x): Compute f(x) = f'(x) f"(x) f""(x) = f(iv)(x) = f(v)(x): = = = = 4 + 4x X We see that the first term does not fit a pattern, but we also see that f(x)(1) = f(1) ƒ'(1) f"(1) = f"" (1) = f(iv) (1) = ƒ(¹)(1) = = = for k ≥ 1.

Let f(x): Compute f(x) = f'(x) f"(x) f""(x) = f(iv)(x) = f(v)(x): = = = = 4 + 4x X We see that the first term does not fit a pattern, but we also see that f(x)(1) = f(1) ƒ'(1) f"(1) = f"" (1) = f(iv) (1) = ƒ(¹)(1) = = = for k ≥ 1.

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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Let f(x) = Compute f(x) fƒ'(x) f"(x) = = = f""(x) = f(iv)(x) = ƒ(v)(x) = 4 + 4x ∞ f(x) = 8 + Σ k=1 X We see that the first term does not fit a pattern, but we also see that f(x)(1) = Hence we see that the Taylor series for f centered at 1 is given by (x - 1)k. f(1) ƒ'(1) f"(1) ƒ""(1) f(iv)(1) = ƒ(¹)(1) = = for k ≥ 1.
Transcribed Image Text:Let f(x) = Compute f(x) fƒ'(x) f"(x) = = = f""(x) = f(iv)(x) = ƒ(v)(x) = 4 + 4x ∞ f(x) = 8 + Σ k=1 X We see that the first term does not fit a pattern, but we also see that f(x)(1) = Hence we see that the Taylor series for f centered at 1 is given by (x - 1)k. f(1) ƒ'(1) f"(1) ƒ""(1) f(iv)(1) = ƒ(¹)(1) = = for k ≥ 1.
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