MATH 2D Study Guide - Midterm Guide: Tangent Space

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2D
• Professor: All

Document Summary

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 (4, 8, 32. At what point does the curve y = ex, < x < + , have maximal curvature? (cid:16) ln. Find the equation of the tangent plane to the surface z = 3x2 y2 + 2x at the point (1, 1, 4). Answer: z 4 = 8(x 1) + 2(y + 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) = 5, and fy(3, 6) = 6.