The extreme values of the function f ( x 1 , x 2 , ⋅ ⋅ ⋅ , x n ) = x 1 + x 2 + ⋅ ⋅ ⋅ + x n subject to the constraint x 1 2 + x 2 2 + ⋅ ⋅ ⋅ + x n 2 = 1 by using Lagrange multipliers.

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