Problem 1: For each of the following functions do the following: (i) Write the function as a piecewise function and sketch its graph, (ii) Write the function as a combination of terms of the from ua t)k(t - a) and compute the Laplace transfornm (a) f(t) = t(1-m(t)) + e'(m(t)-u2(t)) (b) h(t) - sin(2t ) + t4(t)(t/r-sin(2)) + un(t)(2n-t)/r (c) g(t) = uo(t) + Σ.1(-1)kuk(t)