/sci/ - Science & Math

>>9633554
Is this a good proof for the Fourier Transform of a constant?
The only part I'm kind of iffy about is the line towards the middle:
"We have 0/0, which is an indeterminate form, which means we have a nonzero value"

I can't really think of any other way to motivate the fact that the FT of a constant is an impulse

Trying to make proofs of different basic Fourier Transforms, but am running into a problem with the constant function.
The way my professor did it in class was by taking the limit of the two-sided real decaying exponential. I got the same answer he did, but I feel like I did a bunch of handwaving when the frequency is zero.
Is there a better/more rigorous way of solving this one? My proof is in the pic