4. The function f : R - R defined by f(x) = 4x2e-2" is positive, continuous and decreasing on [1, co). Define the series S = En-, f(n). (a) Show for any t E R that f(x) dx = 5e-2 - (2t2 + 2t + 1)e-2t (b) Use the Integral Test and L'Hopital's Rule to determine whether S converges or diverges