Note: no notes, no books, it is not su cient to simply write down the answers. You must explain: you have two hours. how you arrive at your answers. sin2 = Show your work! (a) [5 points] z /4. Determine whether each of the following is convergent or divergent . [10 points] find the rst three terms of the taylor series for the function f (x) = x ln(x2 + 1) with center a = 1 . [5 points] (a) determine the radius of convergence of this power series. [5 points] (b) show that this power series converges for x = 1/3. [5 points] sketch the region in the rst quadrant that lies inside the polar graph r = cos 2 and outside the polar graph r = 1/2. [5 points] determine the area of this region. [10 points] find the volume of the solid obtained by rotating the curve y = ln x for.
