Answered: Exercise 3.3.4: Let f(x) = sin (1/x) if…

Exercise 3.3.4: Let f(x) = sin (1/x) if x = 0, if x = 0. Show that f has the intermediate value property. That is, whenever a y> f(b), then there exists a c = (a, b) such that f(c) = y.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

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Question

Exercise 3.3.4: Let
f(x):=
sin (1/x) if x
10
0,
if x = 0.
Show that f has the intermediate value property. That is, whenever a <b, if there exists a y such that
f(a) ≤ y ≤ f(b) or f(a) >y> f(b), then there exists a c = (a,b) such that f(c) = y.

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