MAC 2312 Midterm: MAC2312 S04 Test 3
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To receive credit, you must show all work. (1) (10 pts. ) If it converges, nd the limit. an = ( 1)nn n2 + 2 (3) (20 pts. ) 1 x dx (4x + 1)2 (4) (10 pts. ) Use the comparison theorem to determine whether the integral is convergent or divergent. 0 p1 + x3 dx (5) let c be the parametric curve de ned by (a) (10 pts. ) Find the equation of the tangent line to c at the point t = 1. T + 1, y = t3 + t + 1, (b) (30 pts. ) Do not evaluate. (iii) set up an integral for the surface obtained by rotating the curve. Let c denote the curve de ned in polar coordinates by the equa- tion.
