I need help with the following problems:

Question 1:

a) Find the Fourier Transform of

b) Determine the limit of this transform as and discuss the result

Question 2:

Solve for Y(x) the integral equation

and verify the solution by direct substitution

Question 3:

Use the time-shift property to calculate the Fourier transform of the double pulse defined by

Question 4:

Given that

a) Draw the graph off(t)

b) Expressf(t)in terms of the Heaviside unit step function

c) Find the Fourier transform off(t)

Thanks in advance for all the valuable help. It is most appreciated.