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Suppose I is an open interval and f € C°(I). Show by induction that ffor х, а € 1, f(x) = f(a) + E%=1f ®)(a)(x – a)/k! + (x – t)"f(n+1)(t)dt

Suppose I is an open interval and f € C°(I). Show by induction that ffor х, а € 1, f(x) = f(a) + E%=1f ®)(a)(x – a)/k! + (x – t)"f(n+1)(t)dt

Advanced Engineering Mathematics
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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Suppose I is an open interval and f € C" (I). Show by induction that ffor х,а € , f(x) = f(a) + E%=1 f(R) (a)(x – a)/k! + - t)"f(n+1)(t)dt %3D k%3D1
Transcribed Image Text:Suppose I is an open interval and f € C" (I). Show by induction that ffor х,а € , f(x) = f(a) + E%=1 f(R) (a)(x – a)/k! + - t)"f(n+1)(t)dt %3D k%3D1
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