(1 point) From a table of integrals, we know that for a, b + 0, Seat eat cos(bt) dt = eat . a cos(bt)+b sin(bt) a² + b² + C. a. Use this antiderivative to compute the following improper integral: or 8 8 cos(2t) est dt = lim T→∞ e³t cos(2t) e-st dt = lim T→∞ if s 3 sin(2T)/2 = ifs 3. help (formulas) b. For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of e³t cos(2t)? (3,infinity) help (inequalities) c. Evaluate the existing limit to compute the Laplace transform of e³t cos(2t) on the domain you determined in the previous part: F(s) = L {e³t cos(2t)} = (s-3)/((s-3)^2+4) help (formulas)