I need to solve a differential, but a portion of the problem is written as a piecewise function with 4 parts, where one part is equal to infinity. I am not sure how to write this using dirac delta. I am not sure if what I tried is correct because there is no answer key. This is review for a test, and I don't want to take the test until I feel confident in what I'm doing.
Any advice on how to rewrite the piecewise function correctly would be helpful. Thank you!
EDIT: I am rewriting the main part I need help with in mathjax
$f(x)=\begin{cases} 0&x<3\\ \infty&x=3\\ 0&3<x<4\\ -2&x\ge 4 \end{cases}$
I would like to know how to rewrite this function using dirac delta. Below is how I attempted to write it, but I'm not sure if I'm doing it correctly.
$f(x)=\delta(x-3)-2u(x-4)$
The full problem is in the image below, but I only wrote the part that I need help with.
