2. (a) Suppose that A CR and A is bounded below with inf(A)=L>0.Prove that for a > 0 and b > 0, the setB = {ax? +by? : x,yE A}is bounded below and inf(B) = (a+b)L².(b) Let D = Q°n ([0, 6] – {x}) C R.i. Find the interior, exterior and boundary of D. Provide a detailedjustification for each answer.ii. Hence, determine whether or not D is a closed set.

Since the posted question has multiple questions but according to guidelines we will solve the first…

Answered: O Suppose that ACR and A is bounded…

O Suppose that ACR and A is bounded below with inf(A) = L> 0. Prove that for a > 0 and b > 0, the set B = {ax² +by² : x,y€ A} is bounded below and inf(B) = (a+b)L².

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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Question

2. (a) Suppose that A CR and A is bounded below with inf(A)=L>0.
Prove that for a > 0 and b > 0, the set
B = {ax? +by? : x,yE A}
is bounded below and inf(B) = (a+b)L².
(b) Let D = Q°n ([0, 6] – {x}) C R.
i. Find the interior, exterior and boundary of D. Provide a detailed
justification for each answer.
ii. Hence, determine whether or not D is a closed set.

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