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

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 71SE: Prove the conjecture made in the preceding exercise.
icon
Related questions
Question
2
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
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage