Please answer question 4 and 5

ECE 250 Lecture2 | Microso | ECE-250 OG Kruskal's DG Kruskal's ~ Messen B Quiz 2 s @ Assignm don as Course Grades - (@) M6-lect OG Graph a |OG Pair in C |OG Graph ir |@ how to i Graph In & ide - En at Membe cpp 2.12- File | C:/Users/Agam/Downloads/assignment7.pdf . . . of 2 + Draw Erase 3. Using the Fourier inversion formula, compute sinc(t) dt. 4. (a) Compute the Fourier transform of f(t) = et. You may use that et dt = VT Hint: Use the integral formula for f(w) and differentiate both sides with respect to w. Now integrate by parts to find a DE which f(w) satisfies.] (b) Compute the Fourier transform of cos(5t) e-. (c) Denote by f(w) the Fourier transform of f(t) = cos(5t)e . Graph f(w) using graphing software (not for marks, for yourself). Find the derivative of f(w) with respect to w (for marks). By examining the derivative, explain why it makes sense that f(w) has local maxima very close to w = 15 5. Exhibit a set of solutions to Uxx(x, t) = 3ut(x, t) which is pairwise linearly independent. That is, your set of solutions should have the property that any two distinct solutions in the set are linearly independent. 6. Solve the system of differential equations dx 1 . . Type here to search O P ~ 96 1) ENG 8:17 PM 2020-03-30