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If you know of good resources (both theories and problems) please let me know!

a) Calculate fourier and inverse fourier transform of f(t).

b) Calculate the limit.

My question is :

it looks like sometimes you use the definition of the transform with the integration of f(t) * e^-iwt ,

other times you use shortcuts from formula sheets. Any tips of when to use which?

I'm pretty clueless about this one right now , is it okay to just ask for a solution with explanation?