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Question

Find the limit (if it exists), limx2x2x2\lim\limits_{x \to 2}\frac{\vert x-2\vert}{x-2}.

Solution

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Answered 1 year ago
Answered 1 year ago
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Recall the definition of the absolute value which states that:

f(x)=x={xifx<0xifx>0\begin{equation*} f(x)=\abs{x}=\begin{cases} -x \quad &\text{if} \, x <0 \\ x \quad &\text{if} \, x>0\\ \end{cases} \end{equation*}

So this means that we are going to solve for the function's limit on both left side and right side of 22.

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