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Problem 4 Suppose the function f has n + 1 derivatives at the point xo, and let = xo + 0x (x − xo) be the intermediate point in Lagrange's formula for the remainder (§) (x − xo)", so that 0 < 0x < 1. Show that 0x → f(n) - 1 termƒ(¹) as x → xo if n! n+1 f(n+1) (xo) 0.

Problem 4 Suppose the function f has n + 1 derivatives at the point xo, and let = xo + 0x (x − xo) be the intermediate point in Lagrange's formula for the remainder (§) (x − xo)", so that 0 < 0x < 1. Show that 0x → f(n) - 1 termƒ(¹) as x → xo if n! n+1 f(n+1) (xo) 0.

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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Problem 4 Suppose the function f has n+1 derivatives at the point xo, and let = xo + x(x − xo) be the intermediate point in Lagrange's formula for the remainder f(n)()(x-xo)", so that 0 < x < 1. Show that 0x 1 term n+1 as x → xo if n! f(n+1) (xo) 0.
Transcribed Image Text:Problem 4 Suppose the function f has n+1 derivatives at the point xo, and let = xo + x(x − xo) be the intermediate point in Lagrange's formula for the remainder f(n)()(x-xo)", so that 0 < x < 1. Show that 0x 1 term n+1 as x → xo if n! f(n+1) (xo) 0.
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