The Dirac delta-function obeys: see image 1a). Prove that: see image 1b). see image 2c). Now briefly describe how this result can be generalised to g(x) with n simple roots at {x1,x2,...,xn} The Dirac delta-function obeysfor any function f(x).a) Prove that[ f(x)d(x − xv)dx = f(xv)·∞where b> 0 is a positive constant.8(bx) =h(r)9 b)=It can be shown that for arbitrary b, 8(bx) = $(), and more generally, 8(b(x − x)) =You can assume these results for this part of the question:8(x-xo)|b|8(x-xo)= |g'(xo)|*i) Consider a function g(x) with one simple root at x = xo. Show that 8(g(x)) =

As per the question we are given the Dirac-delta function δ(x) and we have to prove the following…

Answered: The Dirac delta-function obeys: see…

The Dirac delta-function obeys: see image 1 a). Prove that: see image 1 b). see image 2 c). Now briefly describe how this result can be generalised to g(x) with n simple roots at {x1,x2,...,xn}

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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Question

The Dirac delta-function obeys: see image 1

a). Prove that: see image 1

b). see image 2

c). Now briefly describe how this result can be generalised to g(x) with n simple roots at {x₁,x₂,...,x_n}

The Dirac delta-function obeys
for any function f(x).
a) Prove that
[ f(x)d(x − xv)dx = f(xv)
·∞
where b> 0 is a positive constant.
8(bx) =
h(r)
9

b)
=
It can be shown that for arbitrary b, 8(bx) = $(), and more generally, 8(b(x − x)) =
You can assume these results for this part of the question:
8(x-xo)
|b|
8(x-xo)
= |g'(xo)|*
i) Consider a function g(x) with one simple root at x = xo. Show that 8(g(x)) =

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