(2) Find an example of a function f : [0,1] → R such that f is not continuous, but that f satisfies the conclusion of the Intermediate Value Theorem.
(2) Find an example of a function f : [0,1] → R such that f is not continuous, but that f satisfies the conclusion of the Intermediate Value Theorem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
5.3
Please include a formal proof. Thanks!
![Theorem 3.5.2 (Intermediate Value Theorem). Let [a,b] C R be a closed bounded
interval, and let f : [a,b] → R be a function. Suppose that f is continuous. Let r E R.
If r is strictly between f(a) and f(b), then there is some c E (a,b) such that f(c) =r.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8975dae8-fbcb-4b49-8e3a-715e0e53990f%2Fdef6d876-ad63-4f1d-b1bf-c3f64fcfef89%2F478tsx2_processed.png&w=3840&q=75)
Transcribed Image Text:Theorem 3.5.2 (Intermediate Value Theorem). Let [a,b] C R be a closed bounded
interval, and let f : [a,b] → R be a function. Suppose that f is continuous. Let r E R.
If r is strictly between f(a) and f(b), then there is some c E (a,b) such that f(c) =r.
![Exercise 3.5.1.
(2) Find an example of a function f : [0,1] → R such that f is not continuous, but
that f satisfies the conclusion of the Intermediate Value Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8975dae8-fbcb-4b49-8e3a-715e0e53990f%2Fdef6d876-ad63-4f1d-b1bf-c3f64fcfef89%2Ffmucw4g_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 3.5.1.
(2) Find an example of a function f : [0,1] → R such that f is not continuous, but
that f satisfies the conclusion of the Intermediate Value Theorem.
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