\text { 2. }(36 \text { pts }) \text { Let } u(t)=\frac{1}{1+(2 \pi t)^{2}} \text { and } v(t)=e^{-|t|} \text {. Express all answers with both an exact analytic

expression } and a decimal approximation. (a) Find the smallest frequency bands that contain 90%, 99%, and 99.9% of the energy of u. Do the same for v. (b) Find the frequency bands where |U(f)|2 is at least c times the maximum value of |U(f)|² forcE {0.1,0.01, 0.001}. Do the same for V.