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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}

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
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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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}

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
Transcribed Image Text: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)) =
Transcribed Image Text: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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