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1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e2x, a = 0 b) f(x) = lnx, a = 1 c) f(x) = ², a = 2 x

1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e2x, a = 0 b) f(x) = lnx, a = 1 c) f(x) = ², a = 2 x

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 be a function with derivatives of all orders throughout some interval containing a as an interior point. Then the Taylor series generated by f(x) at x = 0 is: f" (0) f"" (0) 3! f(x) = f(0) + f'(0) 1! 2! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + f'(a) 1! x + d) f(x) = sinx, a = 7 e) f(x)=√x, a = 4 (x − a) + f" (a) 2! -x² + (x − a)² + - -x3 f"" (a) 3! + ... ·(x − a)³ + ... - 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e²x, a = 0 b) f(x) = lnx, a = 1 c) f(x) = ², a = 2
Transcribed Image Text:Let f be a function with derivatives of all orders throughout some interval containing a as an interior point. Then the Taylor series generated by f(x) at x = 0 is: f" (0) f"" (0) 3! f(x) = f(0) + f'(0) 1! 2! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + f'(a) 1! x + d) f(x) = sinx, a = 7 e) f(x)=√x, a = 4 (x − a) + f" (a) 2! -x² + (x − a)² + - -x3 f"" (a) 3! + ... ·(x − a)³ + ... - 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e²x, a = 0 b) f(x) = lnx, a = 1 c) f(x) = ², a = 2
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