MATH 20C Study Guide - Midterm Guide: Tangent Space, Unit Vector, Minimax
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1. f (x, y) = xy2 xy + 3x3y, p = (1, 3). Find the equation of the tangent plane at p: f (x, y) = xe3y ye3x, r(t) = (cid:104)et, ln(t)(cid:105). Find d dt (f r(t)) at t = 1. If v = r(cid:48)(1), nd dvf|p where: find a unit vector u at p = (0, 0, 1) pointing along a direction in which f (x, y, z) = xz + e x2+y. 4 + y2 maximum area: prove: (cid:82)(cid:82, sketch the domain d and evaluate(cid:82)(cid:82) D (hint: choose the appropriate order of integration. : find(cid:82)(cid:82) 1+xy where 0 x 1 and 0 y 1.
