MAC 2312 Midterm: MAC2312 C08 Test 3
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Instructions: write your complete solutions on your answer paper. Do not write on this paper. (1) (30 points) in the (r, )-plane, let c1 denote the curve with equation r = Do not evaluate. (d) write an integral for the area of the region that lies inside c1 and outside c2. Do not evaluate. (2) (20 points) determine whether the integral converges, or diverges. X + 1 dx x2 + 4 (3) (10 points) use a comparison test to determine whether the integral con- verges, or diverges. Z ex + 8 (4) (10 points) evaluate the limits. dx. 0 (a) lim e x sin x x (b) lim x ln (5x) ln (x + 5) (5) (20 points) determine whether the sequence converges or diverges. Find the limit of each convergent sequence. (a) sn = ( 1)n n! n + 1(cid:19)n (b) sn = (cid:18) n + 2.
