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Let S be a closed n-cube with v(S) > 0 and suppose f : S –→ R is continuous on S (relative to S). (a) Prove that infs ƒ and sups f both exist, and that infs f < „IS Js f < sups f. v(S) (b) Prove that there exists xo E S such that f(xo) v(S)

Let S be a closed n-cube with v(S) > 0 and suppose f : S –→ R is continuous on S (relative to S). (a) Prove that infs ƒ and sups f both exist, and that infs f < „IS Js f < sups f. v(S) (b) Prove that there exists xo E S such that f(xo) v(S)

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Let S be a closed n-cube with v(S) > 0 and suppose f : S → R is continuous on S (relative to S). (a) Prove that infs f and sups f both exist, and that infs f < „S) Js f < sups f. v(S) (Ъ) Prove that there exists xo E S such that f(xo) = „S) Js f.
Transcribed Image Text:Let S be a closed n-cube with v(S) > 0 and suppose f : S → R is continuous on S (relative to S). (a) Prove that infs f and sups f both exist, and that infs f < „S) Js f < sups f. v(S) (Ъ) Prove that there exists xo E S such that f(xo) = „S) Js f.
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