MATH 2D Study Guide - Midterm Guide: Tangent Space
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MATH 2D Full Course Notes
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A particle starts at the origin with initial velocity i+ j k. Answer: r(t) =< t3 + t, t4 + t, t3 t > Let c be the curve of intersection of the parabolic cylinder x2 = 2y and the surface 3z = xy. Find the exact length of c from the origin to the point (2, 2, 4. At what point does the curve y = ln x, 0 < x < + , have maximal curvature? (cid:16) Find the equation of the tangent plane to the surface z = 3x2 y2 + 2x at the point (1, 0, 5). Answer: z 5 = 8(x 1) Suppose z = f (x, y), where x = g(s, t), y = h(s, t), g(1, 2) = 3, gs(1, 2) = 1, gt(1, 2) = 4, h(1, 2) = 6, hs(1, 2) = 5, ht(1, 2) = 10, fx(3, 6) = 9, and fy(3, 6) = 2.