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yz (a) Determine whether the limit lim (z,y,2)(0,0,0) r² + 4y² + 9z² exists. If it exists, find the limit.

yz (a) Determine whether the limit lim (z,y,2)(0,0,0) r² + 4y² + 9z² exists. If it exists, find the limit.

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(a) Determine whether the limit lim (z,y,2)-(0,0,0) r² + 4y? + 922 exists. If it exists, find the limit. (b) Given f(x, y) = 5 – xª + 2x² – y². (i) Find the three critical points of the function f. (ii) Classify each critical point as a local maximum, a local minimum or a saddle point using the Second Derivatives Test. (c) Find the maximum value and minimum value of the function f(x, y, z) = 22 – x² – y² on the set S = {(x, y, 2) E R³ | x² + 4y? + 9z² < 36.}.
Transcribed Image Text:(a) Determine whether the limit lim (z,y,2)-(0,0,0) r² + 4y? + 922 exists. If it exists, find the limit. (b) Given f(x, y) = 5 – xª + 2x² – y². (i) Find the three critical points of the function f. (ii) Classify each critical point as a local maximum, a local minimum or a saddle point using the Second Derivatives Test. (c) Find the maximum value and minimum value of the function f(x, y, z) = 22 – x² – y² on the set S = {(x, y, 2) E R³ | x² + 4y? + 9z² < 36.}.
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