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Need help with these, please do not copy from other sources they might be incorrect.

3 2 0 -2 -3 -3 -2 -1 0 1 2 33 2 0 -1 -2 -3 -3 -2 -1 0 1 2 3(3) Let F : R" -> R be a vector field with scalar curl equal to x. Which of the diagrams below better represents ? (i) (ii) (b) For each vector field depicted above, write down a scalar function that seems to describe the divergence of . Justify your answer.(4) Consider the scalar function f(a:,y,z) =m2 :cy+yz+z2 +2 on the region M: {(m,y,z):z2 +y2 +7.2 4}. (3) Find the critical points of f inside M and classify them as local min, local max or saddle pt. (b) Now nd the maximum and minimum values off on the portion of M on the xy plane. This is the equator disk: S: {(93,113) :$2+y2 54% whose boundary BS is a circle of a radius 2. (c) Now use the method of Lagrange multipliers to nd the maximum and minimum values of f in the whole region M, listing all points at which those values occur. Note: feel free to use a calculator for part (c). lf you use decimal expansion for the numbers, please use 3 decimal places