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a) f(x) = e2x, a = 0 e2x = 1+ 2x + 2x²

a) f(x) = e2x, a = 0 e2x = 1+ 2x + 2x²

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) f" (0) f(x) = f(0) + -x+ 1! 2! 3! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + f'(a) 1! TT d) f(x) = sinx, a = 4 e) f(x)=√x, a = 4 -(x − a) + - f" (a) 2! 1 ·(x-a)² + X -x² +· 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e²x, a = 0 e2x = 1 + 2x + 2x² b) f(x) = lnx, a = 1 c) f(x)= = 1, a = 2 = H|2 -x³ + In x = (x − 1) - (x − 1)² - f" (a) 3! 1 4 ... - (x − a)³ + ... (x-2)+ (x-2)² √2 2 sin x = = 1/2² + ²/²2 (x - ²) - ²/² ( x - 7² √x=2+¹(x-4)-¹(x-4)² 64
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) f" (0) f(x) = f(0) + -x+ 1! 2! 3! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + f'(a) 1! TT d) f(x) = sinx, a = 4 e) f(x)=√x, a = 4 -(x − a) + - f" (a) 2! 1 ·(x-a)² + X -x² +· 1. Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. a) f(x) = e²x, a = 0 e2x = 1 + 2x + 2x² b) f(x) = lnx, a = 1 c) f(x)= = 1, a = 2 = H|2 -x³ + In x = (x − 1) - (x − 1)² - f" (a) 3! 1 4 ... - (x − a)³ + ... (x-2)+ (x-2)² √2 2 sin x = = 1/2² + ²/²2 (x - ²) - ²/² ( x - 7² √x=2+¹(x-4)-¹(x-4)² 64
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