Let I (a, b) be a bounded open interval and f: I R be a monotone increasing function on I. (i) If f is bounded above on I, then lim f(x) = sup f(x). xE (a,b) %3D (ii) If f is bounded below on I, lim f(x) = x a+ inf f(x). xE (a,b) then
Let I (a, b) be a bounded open interval and f: I R be a monotone increasing function on I. (i) If f is bounded above on I, then lim f(x) = sup f(x). xE (a,b) %3D (ii) If f is bounded below on I, lim f(x) = x a+ inf f(x). xE (a,b) then
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Prove. ii.
Transcribed Image Text:Let I = (a, 6) be a bounded open interval and f :I →
%3D
R be a monotone increasing function on I.
(i) If f is bounded above on I, then lim f(x)
sup f(x).
πε (α,)
x→b-
(ii) If f is bounded below on I, then lim f(x) :
inf f(x).
xE (a,b)
x-- a+
(iii) If f is unbounded above on I, then lirn f(x)
(iv) If f is unbounded below on I, then lim f (x)
X -- a+
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