APPM 1360 Final: appm1360summer2017examfinal
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Summer 2017: (20 pts) consider the curve described parameterically by x(t) = t 2 and y(t) = ln(sec t) with 0 t < /2. Find the length of this curve between the points whose y-coordinates are 0 and 1. You need not simplify your nal answer: (10 pts) find an antiderivative of. 0 about y = 1: (10 pts) sketch the graph of 9x2 18x + 4y2 = 27, properly labeling the vertices. 1 x ex = sin x = cos x = tan 1 x = ln(1 + x) = (1 + x)k = Xn=0 xn xn n! (2n + 1)! (2n)! ( 1)n x2n+1 ( 1)n x2n ( 1)n x2n+1 ( 1)n 1 xn (cid:18)k n(cid:19)xn n (2n + 1) Rn(x) = f (n+1)(z) (n + 1)! (x a)n+1. Center of mass/centroid integrals m = z b. Mn = x [f ( x1) + f ( x2) + + f ( xn)] where x =
