a) Show that if f(x) has a finite jump discontinuity at x=a, then F(f′(x))=AF(ω)+B[f(a+)−f(a−)]e−iωa, in which F stands

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a) Show that if f(x) has a finite jump discontinuity at x=a, then F(f′(x))=AF(ω)+B[f(a+)−f(a−)]e−iωa, in which F stands for the Fourier Transform, and A and B are constants. Also, find A and B b) Find the Fourier Transform of f′(x) if f(x)={x0​ if 0≤x<1 otherwise ​ PROBLEM 3 1. Use the Laplace Transform to solve the following initial-value problems: a) dt2d2f​−dtdf​−2f=e−tsin2t,f(0)=0,f′(0)=2 b) dt2d2f​−3dtdf​+2f=⎩⎨⎧​010​ if t∈[0,3) if t∈[3,6] if t>6​ with f(0)=0,f′(0)=0