(a) Recall from class that F (eikx) = √2πd(w – k). If F(cos(10x + 2)) √√(AS(w - 10) + -AG(w)) then find the complex numb

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(a) Recall from class that F (eikx) = √2πd(w – k). If F(cos(10x + 2)) √√(AS(w - 10) + -AG(w)) then find the complex number A and the function G(w). Use I for the imaginary unit √-1 and delta for the function. V A = G(w) P (b) Let f(x) = ∞ wsin(wx) 4+w2 -dw for x > 0. JO Find f(x). Hint: Consider the Fourier sine transform of f(x), and try functions of the form f(x) = exp(-ax). You can use W -ax 6.⁰⁰ sin(wx) dx = for a > 0. a² + w² f(x) = (c) Hence evaluate 6° ∞ wsin(wx) w² du for x = -0.15. Give your answer correct to 2 decimal places. Number = =