. Consider the function f: R→ [0, 1] defined by f(x) = 1 if x is rational, and f(x) = 0 if * is irrational. For which values of a € R does lima f(x) exist? At which values of a € R is f continuous?
. Consider the function f: R→ [0, 1] defined by f(x) = 1 if x is rational, and f(x) = 0 if * is irrational. For which values of a € R does lima f(x) exist? At which values of a € R is f continuous?
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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![Consider the function \( f : \mathbb{R} \to [0, 1] \) defined by \( f(x) = 1 \) if \( x \) is rational, and \( f(x) = 0 \) if \( x \) is irrational. For which values of \( a \in \mathbb{R} \) does \( \lim_{x \to a} f(x) \) exist? At which values of \( a \in \mathbb{R} \) is \( f \) continuous?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e8ed93-7bef-4409-89ed-52264f64a27e%2Fee2d71f4-f1e0-4318-b599-634155163daa%2F11yivq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function \( f : \mathbb{R} \to [0, 1] \) defined by \( f(x) = 1 \) if \( x \) is rational, and \( f(x) = 0 \) if \( x \) is irrational. For which values of \( a \in \mathbb{R} \) does \( \lim_{x \to a} f(x) \) exist? At which values of \( a \in \mathbb{R} \) is \( f \) continuous?
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