i want you to solve part C. remember from b, use the conclusion there, try to show as x in this open ball apporaching unit sphere, f should go to infinity. you prove that all boundary points goes to infinity. 4. (a) Let A CR" be a set such that A ‡ Ø. Let ε : A → (0, ∞) be a function on A taking values inthe positive reals. Prove that A \ (U₁€@A Bɛ(a)(a)) is closed.(b) Let A CR" be non-empty, open, and bounded. Let ƒ : A → R be a continuous function such thatlim f(x) = ∞ for all a € A. Prove that f attains its minimum on A.x→a(e) Consider the function ƒ : B₁(0) → R given by the formula ƒ(x₁, 72, 73) = £₁ + e¹---¹--³. Provethat f attains its minimum on B₁ (0) but does not attain its supremum on B₁(0).

Answered: Image /qna-images/answer/9e4ace54-0276-4f3f-afe6-312119e5718b.jpg

Answered: Prove (c) Consider the function ƒ :…

Prove (c) Consider the function ƒ : B₁(0) → R given by the formula ƒ(T₁, T2, T3) = £₁ + e¹--1--3--} . that f attains its minimum on B₁ (0) but does not attain its supremum on B₁ (0).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

i want you to solve part C. remember from b, use the conclusion there, try to show as x in this open ball apporaching unit sphere, f should go to infinity. you prove that all boundary points goes to infinity.