Talyor series for f(x) about x = a is, f(m (a) f(x) = (x – a)" п! n=0 = f(a) + f'(a)(x – a) + f"(a) (x – a)² + 2! f''(a) (x – a)³ + .* (x- a)³ + .. 3! - (a) Find the Talyor Series for f(x) = e* about x = 0. (b) Find the Talyor Series for f(x) = In (x) about x = 2. %3D
Talyor series for f(x) about x = a is, f(m (a) f(x) = (x – a)" п! n=0 = f(a) + f'(a)(x – a) + f"(a) (x – a)² + 2! f''(a) (x – a)³ + .* (x- a)³ + .. 3! - (a) Find the Talyor Series for f(x) = e* about x = 0. (b) Find the Talyor Series for f(x) = In (x) about x = 2. %3D
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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Transcribed Image Text:4. Talyor series for f(x) about x = a is,
f(x) = Sf®(a)
(x – a)"
n!
n=0
f"(a)
f''(a)
= f(a) + f'(a)(x – a) +
(x – a)² + :
2!
(x – a)3 + ...
3!
(a) Find the Talyor Series for f(x) = e* about x = 0.
(b) Find the Talyor Series for f (x) = In (x) about x = 2.
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