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MAT 21C Lecture Notes - Lecture 22: Tangent Space, Tangent, Open Set

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burgundywombat446

13 Dec 2018

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MAT 21C Full Course Notes

MAT 21C Full Course Notes

Document Summary

Announcements: m 11/28 from 3:10-4pm 204 art, w 11/30 6:10-8pm 6 olson, r 12/1 for 4:10-5pm 6 wellman. The tangent plane at the point p0(x0, y0, z0) on the level surface f (x, y, z) = c of a di erentiable function f is the plane through p0 normal to f |p0 . Rule (tangent plane to a level surface f (x, y, z) = c at p0(x0, y0, z0)). fx(p0)(x x0) + fy(p0)(y y0) + fz(p0)(z z0) = 0. The normal line of the surface at p0 is the line through p0 parallel to f |p0 . Rule (normal line to a level surface f (x, y, z) = c at p0(x0, y0, z0)). x = x0 + fx(p0)t, y = y0 + fy(p0)t, z = z0 + fz(p0)t. The linearization of a function f (x, y) at a point (x0, y0) where f is di erentiable is the function.

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Related Questions

Can someone help me do the question 1(b),2(b)? thx

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