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Calculus III. Please show all work and mark the answer(s)! 1) Use Lagrange multipliers to find...

Calculus III. Please show all work and mark the answer(s)!

1) Use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = x^2 + y^2 subject to the constraint xy = 1.

2) Use Lagrange Multipliers to find the point on the curve 2x + 3y = 6 that is closest to the origin. Hint: let f(x, y) be the distance squared from the origin to the point (x, y), then find the minimum of f subject to the constraint that the point (x, y) must be on the given curve.

Thank you in advance.

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