Midterm 2 MAT3320 - Fall 2021 due date: Thursday November 18 by 11:59 pm: upload it on brightspace Question 1. The Fourier transform of a function f(x) (x ( R) is f ( K ) = = V2TT e -ikx f(x)dx Prove the following (see Frame 20) F' ( k ) = ikf ( k ) Hint: assume that lim f(x) = 0, and use integration by parts. You may 1-+100 have studied a similar exercise in MAT2384 (Laplace transform). Question 2. Determine if the Fourier transform of f(x) exits or not. It it exists, compute it. a) f(1) = ex b) f (I ) = 3 Ja if la