MAC 2312 Midterm: MAC2312 S03 Test 3
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Instructions: write your complete solutions in your exam book. To receive credit, you must show all work. (1) (10 pts. ) Find the limit: lim x 0 ex 1 x x2 (2) (20 pts. ) If it converges, nd the limit. (a) an = 4n (b) an = ( 1)nn n + 2 (3) (20 pts. ) 0 (a) z 2 (b) z ln x dx. Use the comparison theorem to determine whether the integral is convergent or divergent. Let c be the parametric curve de ned by x = 2 + 3t + t2, y = 2(t + 1)et, Find the equation of the tangent line to c at the point t = 0. (6) (30 pts. ) Let c denote the curve de ned in polar coordinates by the equa- tion r = 2 + cos where 0 2 .
