Write your solutions coherently on the paper provided. You are not required to simplify your answers. You must say why a given series or integral diverges or converges. (1) (20 pts. ) Let c be the curve de ned in polar coordinates by the equation r = 1 cos 2 , 0 . (a) sketch the curve in the xy-plane. Use an arrow to indicate the direction of motion as increases. (b) set up and evaluate an integral for the area of the region enclosed by. Evaluate the limit, or show that it does not exist. lim x 0+ x3 ln x (4) (10 pts. ) If it con- verges, nd its value. (5) (15 pts. ) Find the antiderivatives: dx (a) z (b) z. Determine whether the in nite series converges or diverges. If it converges, nd the sum. n (cid:19) n 1 n + 1 (a)
