Let S be a closed n-cube with v(S) > 0 and suppose f : S → R is continuous on S (relativeto 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.

let S be a closed n-cube with vS>0 and suppose f:S→R is continuous on S (a) prove that infSf and…

Answered: Let S be a closed n-cube with v(S) > 0…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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)