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Example 1: If the value of the function f(x) and all its derivatives are known at the point x, find the value of this function at the points x+h and x-h.

Example 1: If the value of the function f(x) and all its derivatives are known at the point x, find the value of this function at the points x+h and x-h.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Taylor Series Example 1: If the value of the function f(x) and all its derivatives are known at the point x, find the value of this function at the points x+h and x-h. Solution: Taylor series is f(x) = f (a) + (x – a)f'(a) + *-a) f"(a) +. (v-x) 2! Here we have a = x- f(x+h)% 3D f(x)+((x+h)-x)f'(x) + ((x+h) – x)* )+ ((x+h)– x)' f"(x)+... 2! 3! h? = f(x) + h.f'(x) + , f"(x) + f"(x) +.. h 3! f(x-h) = f(x)+((x-h)- x)f'(x) + ((x-h) – x)* )+ (x – k) – x)' 2! 3! **** + (x).f. h? h = f(x)- h.f'(x) +f"(, 3! 2!
Transcribed Image Text:Taylor Series Example 1: If the value of the function f(x) and all its derivatives are known at the point x, find the value of this function at the points x+h and x-h. Solution: Taylor series is f(x) = f (a) + (x – a)f'(a) + *-a) f"(a) +. (v-x) 2! Here we have a = x- f(x+h)% 3D f(x)+((x+h)-x)f'(x) + ((x+h) – x)* )+ ((x+h)– x)' f"(x)+... 2! 3! h? = f(x) + h.f'(x) + , f"(x) + f"(x) +.. h 3! f(x-h) = f(x)+((x-h)- x)f'(x) + ((x-h) – x)* )+ (x – k) – x)' 2! 3! **** + (x).f. h? h = f(x)- h.f'(x) +f"(, 3! 2!
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