Question

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

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 5Recall the definition of the absolute value which states that:

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

So this means that we are going to solve for the function's limit on both left side and right side of $2$.

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