MAT 397 Study Guide - Midterm Guide: Tangent Space, Integral, Iterated Integral
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Instructor: biermann, bourhim, choi, fatica, griffin (circle one) Instructions: there are a total of 8 pages (including this one). Please check to see that you have all. Do all your work on this examination: a scienti c graphics calculator may be used on this nal. Points (10) (10) (10) (10) (10) (10) (10) (10) (10) (10) (15) (10) (125) 2: let c be the curve given by r(t) = t(t + 3)i sin tj + e2tk. Find the parametric form of the equation of the line tangent to c at (0, 0, 1): find the equation of the tangent plane to the surface z = ye x at the point (0, 1, 1). 3: assume z(s, t) = f (x(s, t), y(s, t)). 0 f (x, y) dydx as an iterated integral with the order of integration reversed: evaluate z z (y2. X2) da where d is the region bounded by the curves y x = 1,
