GIve a function that meets the requirements of b and PROVE why it works (a) A function f : R → R that is continuous only at x = 0 and r = 1.(b) A bounded, 3B > 0 such that |f(x)| < B Vx e (0, 1), continuous function on (0, 1) withunbounded derivative on (0, 1).

Answered: A bounded, 3B > 0 such that |f(x)| < B…

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A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded derivative on (0,1).

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

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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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

GIve a function that meets the requirements of b and PROVE why it works

(a) A function f : R → R that is continuous only at x = 0 and r = 1.
(b) A bounded, 3B > 0 such that |f(x)| < B Vx e (0, 1), continuous function on (0, 1) with
unbounded derivative on (0, 1).

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