1. Transform the following Eulers equation 2dy - 4r dy 4 + 5y = Inr into a second order linear DE with constant coefficients by making the sub- stitution r = e' and solve it. 2. Determine if the following series converge; if they do, find their sum. (a) n= 1 (b) iM n- + 3n + 2 3. (a) Find a power series for the function f : (0, co) - R given by f(x) = cos + about the point I = T. (b) Find the Taylor series for the function f : (0, co) - R given by /(x) = e2z about the point r = 0. 4. Plot the functions y1 : R - R, y2 : R - R given by y(x) = 1 -r and w(r) = r. Compute the area bounded by the graphs of y, and yz and the horizontal axis. 5. Plot the polar curves ri(0) = 2sine and ra(0) = 1. Write the formula for the area inside , but not inside r2. Compute the integral if you want an extra point