Calculate , f(x, y, z) dS For Part of the surface x = z', where 0 < x, y < 13-2; f(x, y, z) = Is f(x, y, z) dS =

a) Compute the equation of the tangent plane to the level surface g(x, y, z) = x'y + 2y°z – 3z*x = 3 Don't round answers unless at the point (1,0, – 1). b) Consider z = z(x, y) as a function of x and y, so z(1,0) = -1. Use the approximation of the surface by its tangent plane to approximate 21 = z(0.99, 0.02). c) Use your approximation of z1 from part b to evaluate g(0.99, 0.02, zı) to five decimal places. Your answer should be close to 3. Is it? the instructions request approximations, or as part of checking your own work.

A differentiable function f(x, y) has the property that f(1, 3) = 2 and fz(1, 3) = 6 and fy(1, 3) = 3. Find the equation of the tangent plane at the point on the surface z = f(x, y) where x = 1, y = 3. 2 =

a surface is defined by the parametric form. S(u,v)= X(u,v)i + Y(u,v)j + Z(u,v)k, where 0<= u <=2pi and 0<= v <=1 X(u,v) = (v2+1)cos2u Y(u,v) =vsinu Z(u,v) =-(v2+1) a. determine the normal vector of the surface S b. determine the unit normal vector of S(0,1/2) that point onward