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Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at a. 2r π d) f(x) = sinx, a = 7 e) f(x) = √√√x, a = 4 4

Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at a. 2r π d) f(x) = sinx, a = 7 e) f(x) = √√√x, a = 4 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) 3! f'(0) f(x) = f(0) + -x+ 1! 2! f(x) at x = a is: And the Taylor series generated f(x) = f(a) + f'(a) 1! +2 TT d) f(x) = sinx, a = 4 e) f(x)=√x, a = 4 + f" (a) (x a) + ·(x − a)² + 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.
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) 3! f'(0) f(x) = f(0) + -x+ 1! 2! f(x) at x = a is: And the Taylor series generated f(x) = f(a) + f'(a) 1! +2 TT d) f(x) = sinx, a = 4 e) f(x)=√x, a = 4 + f" (a) (x a) + ·(x − a)² + 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.
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