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Using Lagrange multipliers, find the min and max distance from the point P(0, 1, 0) to the ellipsoid 2x + y + z =

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Using Lagrange multipliers, find the min and max distance from the point P(0, 1, 0) to the ellipsoid 2x + y + z = 6, and also find where the min/max distance is attained on the ellipsoid. You can assume that the absolute extrema must exist and be attained only at the candidate points determined by Lagrange multipliers.

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