Consider the function: { 0 ;if x is rational ; if x is irrational f(x) = Use a d, e argument to prove that f(x) is continuous at any point x = 0.
Consider the function: { 0 ;if x is rational ; if x is irrational f(x) = Use a d, e argument to prove that f(x) is continuous at any point x = 0.
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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Class: Mathematical Analysis/
![Consider the function:
\[
f(x) =
\begin{cases}
0 & \text{; if } x \text{ is rational} \\
x & \text{; if } x \text{ is irrational}
\end{cases}
\]
Use a \(\delta, \epsilon\) argument to prove that \(f(x)\) is continuous at any point \(x = 0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa9c753-6b68-41b4-8837-61aa8aa0a19b%2Fa6d7fbf9-5c11-486c-8bc5-faf80aef66f1%2Fen0g64d_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function:
\[
f(x) =
\begin{cases}
0 & \text{; if } x \text{ is rational} \\
x & \text{; if } x \text{ is irrational}
\end{cases}
\]
Use a \(\delta, \epsilon\) argument to prove that \(f(x)\) is continuous at any point \(x = 0\).
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