MAC 2312 Midterm: MAC2312 S04 Test 4
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To receive credit, you must show all work. (1) (30 pts. ) 1 + x (a) z (b) z 4x2 4x 2 x(x2 1) (c) z sin3(x/2) dx = dx = (3) (20 pts. ) 1 + x2 dx x (4) (10 pts. ) Let c be the parametric curve de ned by x = 2t3, y = 3t2, Set up, but do not evaluate, an integral for the length of c. (5) (10 pts. ) If it converges, nd the limit. an = ( 1)nn3 en. For the following, determine whether the series converges or di- verges. For each convergent series, nd the sum. (a) 6 (b) 2 1 + 1 1 + 1 1 + . n + 1 n (cid:19) (c) (d) 3 + For the following, determine whether the series converges abso- lutely, converges conditionally, or diverges. (a) (b) (c) N3 + 1 ( 2)n n3 + 1 ( 1)n.
