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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) = =, a = 2 d) f(x) = sinx, a = 7 4 e) f(x)=√x, a = 4

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) = =, a = 2 d) f(x) = sinx, a = 7 4 e) f(x)=√x, a = 4

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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Solve 1B and 1C 

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: ƒ'(0) f(x) = f(0) + -x + 1! f"(0) f"" (0) -x² +: 3! 2! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + 1 == a = 2 ) f'(a) 1! c) f(x) = f"(a) 2! 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 π d) f(x) = sinx, a = = 4 e) f(x) = √x, a = 4 -x³ + (x − a) + -(x − a)² + · (x − a)³ + · f""'(a) 3!
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: ƒ'(0) f(x) = f(0) + -x + 1! f"(0) f"" (0) -x² +: 3! 2! And the Taylor series generated by f(x) at x = a is: f(x) = f(a) + 1 == a = 2 ) f'(a) 1! c) f(x) = f"(a) 2! 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 π d) f(x) = sinx, a = = 4 e) f(x) = √x, a = 4 -x³ + (x − a) + -(x − a)² + · (x − a)³ + · f""'(a) 3!
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