(Q5) Your acquaintance Dr Zookh is very excited because she believes that she has proved the following result. Theorem (Zookh's Boundedness Theorem). Every continuous function f: R+R is bounded. That is, the set {f(x): r ER} is bounded above and below. Proof. Let f: R→ R be continuous. Then f is continuous at 0. Denote the value of f(0) by y. Since f is continuous at 0, we may let € = 1 and conclude that f(x) - y = f(x)-f(0)| <= 1 for all z € R. Thus y-1
(Q5) Your acquaintance Dr Zookh is very excited because she believes that she has proved the following result. Theorem (Zookh's Boundedness Theorem). Every continuous function f: R+R is bounded. That is, the set {f(x): r ER} is bounded above and below. Proof. Let f: R→ R be continuous. Then f is continuous at 0. Denote the value of f(0) by y. Since f is continuous at 0, we may let € = 1 and conclude that f(x) - y = f(x)-f(0)| <= 1 for all z € R. Thus y-1
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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