Basic Analysis I — Real Analysis · Problem 3.2.5

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Define f:R→Rf : \mathbb{R} \to \mathbb{R} by f(x):={xsin⁡(1/x)if x≠0,0if x=0.f(x) := \begin{cases} x\sin(1/x) & \text{if } x \neq 0, \\ 0 & \text{if } x = 0. \end{cases} Is ff continuous? Prove your assertion.

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