MAC 2312 Midterm: MAC2312 F14 Test 3
Document Summary
Write your complete solutions on your answer paper. (1) (15 pts. ) Find the limits: (a) lim x 0+ x2 ln x (b) lim x 1 (c) lim x (x 1)2 x2 + 1 sin x x (2) (15 pts. ) If it diverges, explain why. (a) an = (b) an = (c) an = ( 1)n3n+1. 2n ( 1)n n + 1 n2 + 10100 n2 + 2n 1 (3) (30 pts. ) If it diverges, explain why. (a) z 6 (b) z . X 5 (x + 1)(x 2) For the curve c de ned by polar equation r = 1 sin , answer the following. (a) sketch the curve in the xy-plane. Indicate by an arrow the direction in which the curve is traced as increases. (b) set up an integral for the area of the region enclosed by c. do not evaluate. (5) (25 pts. )
