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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Answered: . Consider the function f: R→ [0, 1]…

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: 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?