MATH 234 Lecture Notes - Lecture 13: Tangent Space

• School: UW-Madison
• Department: Mathematics
• Course: MATH 234
• Professor: Betsy Stovall

Document Summary

X= xo + x , y = yo + y. F dfdx (xo, y1) x + dfdy (xo, yo) y. X = x xo , y = y yo zo = f(xo, yo) Ea of the tangent plane z = f(xo, yo) + dfdx (xo, y1)(x xo) + dfdy (xo, yo)(y yo) The point (xo, yo, zo) lies on the upper half of the sphere of radius 3 centered at the origin (0, 0, 0) General eq. of a sphere of radios r centered at the point (a, b, c) (x a)2 + (y b)2 + (z c)2 = r2. In the example x2 + y2 + z2 = 32. (cid:885)(cid:884) x(cid:884) y(cid:884) fy(x, y) = fx(2, 2) = (cid:884)(cid:883) = 2. For upper half: fx(x, y) = z2 = 3 x2 42. For upper half space (z (cid:3410) 0) z = (cid:885)(cid:884) x(cid:884) y(cid:884)