MATH 141 Study Guide - Final Guide: Conditional Convergence, Cartesian Coordinate System, Taylor Series
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5. (5 points) find f(cid:48)(x) if f (x) = xsin(x). Final exam, sample d (cid:19) (cid:19) xsin(x) xsin(x) + cos(x) ln x: f(cid:48)(x) = cos(x)xsin(x, f(cid:48)(x) , f(cid:48)(x) , f(cid:48)(x) = (cid:18) cos(x) cos(x) (cid:18) sin(x) x x x (cid:90) . 4: f(cid:48)(x) = sin(x)xsin(x) 1, (5 points) evaluate a) b) c) d) e) 4 x3 + 2x2 dx: 1 1 e, 1. 2e: 1 e, 1 2 e, 0 (cid:90) (cid:12)(cid:12)(cid:12)(cid:12) + (cid:12)(cid:12)(cid:12)(cid:12) 2. 2 x (cid:12)(cid:12)(cid:12)(cid:12) x 2 (cid:12)(cid:12)(cid:12)(cid:12) x + 2 x + 1 x: 4 ln |x3 + 2x2| + c, ln, ln x, ln |x + 2| 2 x, 2 ln |x + 2| + Math 141, 141h: (5 points ) evaluate lim x . 2: the limit does not exist. (cid:19) (cid:18) 3 x, (5 points) evaluate lim x x sin, 1, 3 c) 3: 0, (5 points) evaluate lim x ln (2 + ex)
