Could you teach me how to show (ii), (iii) in detail? Let A be a non-empty subset of a metric space (X,d) and x an element of X.Define the distance from x to A asd(x, A)inf{d(x, a): a € A}.(i) Prove that the function ƒÃ :fA:X → R, defined as ƒ₁(x) = d(x, A) satisfies=|ƒ^(x) - f^(y)] ≤

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Answered: Prove that A = {x : x € X and ƒÃ(x) =…

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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The tangent plane to the graph of the function f(x,y)=x+xy+y2, which is parallel to the z=1+2x+3y plane, and the point of tangency are(Fill in the blanks below): Z= ____ x+_____ y- _____ and ( _____ ,_____ ,_____)
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Prove that A = {x : x € X and ƒÃ(x) = 0}. (iii) Suppose A and B are nonempty disjoint closed subsets of X. Use the function g = fĄ – ƒB to prove that there exist disjoint open sets U and V with ACU and B CV.