Given $$\frac {df}{dx}(x)=\lim\limits_{\Delta x\to0}\frac {f(x+\Delta x)-f(x)}{\Delta x},$$ how do I express using the above expression or test if the limit exists for $$ f(x) = \lvert x-2\rvert?$$
2026-05-05 13:41:29.1777988489
How do I test/check if the limit exists for $f(x) = \lvert x-2\rvert$
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The given function can be written as:
$f(x)=\begin{cases} x-2 & \text{ if } x\geq2 \\ 2-x & \text{ if } x<2 \end{cases}$
Can you do it from here?