Question: QUES'I'ION l The sphere :52 + y2 + 252 : 36 and the plane :1: + y + z : ll} intersect in an ellipse.

QUES'I'ION l The sphere :52 + y2 + 252 : 36 and the plane :1: + y + z : ll} intersect in an ellipse. Use Lagrange multipliers, or any other method, to nd the lowest point (= point with minimal z-value) on this ellipse. QUESTION 2 Find the absolute maximum and absolute minimum values of the function f (2:, y) = (:1: l)2 + y3 33; on the region {(113 y) E R2 : (:r: U2 + (y l)2 <_: hint: to nd the maxinuun and minimum on boundary of this region you might want use lagrange multipliers>

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