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  "body": "\n## Example\n\nLet $f(x) = x \\sin(1/x)$ for $x \\ne 0$, and let $f(0) = 0$.\nThen $f$ is [[continuous|0EEE2CZB2A]] at $0$, and so $f$ is continuous on $\\mathbb{R}$.\nIndeed, $|f(x)| \\le |x|$ for all $x$, so $f(x) \\to 0$ as $x \\to 0$ by the [[squeeze theorem|0XMF00T4XQ]].\n\n## Remarks\n\nThe factor $x$ damps the oscillation of $\\sin(1/x)$.\nThe function is not differentiable at $0$. The difference quotient $(f(x) - f(0))/x = \\sin(1/x)$ has no limit.\nThe function $x^2 \\sin(1/x)$ is [[differentiable with a discontinuous derivative|0WDAKKN4NC]].\n\n## Explanations\n\n### L1 human\n\nThe graph of $x \\sin(1/x)$ oscillates infinitely often near $0$.\nBut it stays between the lines $y = x$ and $y = -x$, which meet at the origin.\n",
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