CAn you give an example with Taylor series approximatio

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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CAn you give an example with Taylor series approximation. I've watched several videos on youtube but still dont understand it

Taylor Series Expansion
Taylor's Theorem : Suppose fis continuous on the closed interval [a, b] and has
n+1 continuous derivatives on the open interval (a, b). If x and c are points in
(a, b), then
The Taylor series expansion of f (x) about c:
f((c)
f(c) + f'(e)(x-c)+ x-c) +© (x-c)'+..
fl) (c)
2!
3!
or
00
1
Taylor Series= (c) (x-c)*
k!
k=0
If the series converge, we can write:
1
f(x) = E f(c) (x-c)*
k!
k-0
Transcribed Image Text:Taylor Series Expansion Taylor's Theorem : Suppose fis continuous on the closed interval [a, b] and has n+1 continuous derivatives on the open interval (a, b). If x and c are points in (a, b), then The Taylor series expansion of f (x) about c: f((c) f(c) + f'(e)(x-c)+ x-c) +© (x-c)'+.. fl) (c) 2! 3! or 00 1 Taylor Series= (c) (x-c)* k! k=0 If the series converge, we can write: 1 f(x) = E f(c) (x-c)* k! k-0
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