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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Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad6d3522-58fe-4a42-a237-8062bf310251%2Ff03e67ca-cb42-4139-800e-6a0030c691b1%2Fvnaczm4_processed.jpeg&w=3840&q=75)
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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