Taylor SeriesExample 1: If the value of the function f(x) and all its derivatives are known at thepoint 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) +..h3!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!

If the value of the function fx and all its derivatives are known at the point x, to find the value…

Answered: Example 1: If the value of the function…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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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.