Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
cx%3D+00 Using only the property f(a) = o f(x)8(x – a)dx as a definition of the Dirac delta, prove the x=-00 following properties of the Dirac Delta rx=+00 i) L 8(x – a)dx = 1 x=-00 = (x) ii) 8-x) ii) а8(tax) —D &х); а > 0 in) 8(x? — а?) %3D - 16(х + а) + 6(х - а)] 2a

cx%3D+00 Using only the property f(a) = o f(x)8(x – a)dx as a definition of the Dirac delta, prove the x=-00 following properties of the Dirac Delta rx=+00 i) L 8(x – a)dx = 1 x=-00 = (x) ii) 8-x) ii) а8(tax) —D &х); а > 0 in) 8(x? — а?) %3D - 16(х + а) + 6(х - а)] 2a

icon
Related questions
Question
100%
Using only the property f(a) = S*** f(x)8(x – a)dx as a definition of the Dirac delta, prove the (x=+00 x=-00 following properties of the Dirac Delta x=+0 i) S S(x – a)dx = 1 x=-00 = (x) ii) 8-x) iii) a(±ax) = (x); a > 0 iv) 8(x² – a²) = [8(x + a) + 8(x – a)] 2a d8(x-a) dx df(x)] x%=+00 v) S f(x)0 x=-00 dx dx x=a
Transcribed Image Text:Using only the property f(a) = S*** f(x)8(x – a)dx as a definition of the Dirac delta, prove the (x=+00 x=-00 following properties of the Dirac Delta x=+0 i) S S(x – a)dx = 1 x=-00 = (x) ii) 8-x) iii) a(±ax) = (x); a > 0 iv) 8(x² – a²) = [8(x + a) + 8(x – a)] 2a d8(x-a) dx df(x)] x%=+00 v) S f(x)0 x=-00 dx dx x=a
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer