3;0i Thus, the equation of the tangent plane at (1;1;1) is 3(x 1) 3(y 1) = 0 =)x y= 0;Question f1(x,y,z) = x^2 y^2 z^2 −1 = 0 f2(x, y, z) = 2x^2 y^2 − 4z = 0 f3(x,y,z) = 3x^2 −4yz^2 = 0 This system can be concisely represented as F(x) = 0, where F(x) = (f1, f2, f3)T , x=(x,y,z)T and 0 = (0,0,0)T (transpose written because these should be column vectors) Using matlab Starting with the initial condition x0 = (05, 0→n dS, where → F = bxy2,bx2y,(x2 y2)z2 and S is the closed surface bounding the region D consisting of the solid cylinder x2 y2 6 a2 and 0 6 z 6 b Solution This is a problem for which the divergence theorem is ideally suited Calculating the divergence of → F, we get → ∇
Level Surfaces
