# Thread: Calculating limit of rational function

1. ## Calculating limit of rational function

For the question in the image, can someone please explain to me why we should interpret $\sqrt{x^2}$ as $|x|$?

2. ## Re: Calculating limit of rational function

$x\geq 0 \Rightarrow \sqrt{x^2} = x\\x< 0 \Rightarrow \sqrt{x^2} = -x\\ \text{This is identical to the definition of }|x|$

3. ## Re: Calculating limit of rational function

graph of $y = \sqrt{x^2}$

4. ## Re: Calculating limit of rational function

The definition of the symbol $\sqrt{x}$ is that it is the positive square root.