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Let S ∈ R3 be the sphere of radius 1 centered on the origin. a) Prove...

Let S ∈ R3 be the sphere of radius 1 centered on the origin. a) Prove that there is at least one point of S at which the value of the x + y + z is the largest possible. b) Determine the point (s) whose existence was proved in the previous point, as well as the corresponding value of x + y + z.

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