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If $f(x)=|x-2|$, then
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Verified Answer
The correct answer is:
$f(x)$ is continuous at $x=2$
$\begin{aligned} & \text {Here } f(2)=0 \\ & \lim _{x \rightarrow 2}^{-} f(x)=\lim _{h \rightarrow 0} f(2-h)=\lim _{h \rightarrow 0}|2-h-2|=0 \\ & \lim _{x \rightarrow 2}^{+} f(x)=\lim _{h \rightarrow 0} f(2+h)=\lim _{h \rightarrow 0}|2+h-2|=0\end{aligned}$
Hence it is continuous at $x=2$.
Hence it is continuous at $x=2$.
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