Evaluate the limit

by RoRi

August 26, 2015

Evaluate

$\lim_{x \to 0^-} \frac{\sqrt{x^2}}{x}.$

For $x < 0$ we have $\sqrt{x^2} = |x| = -x$ . Since we are taking the limit as $x$ approaches 0 through negative values we have

$\lim_{x \to 0^-} \frac{\sqrt{x^2}}{x} = \lim_{x \to 0^-} \frac{-x}{x} = \lim_{x \to 0^-} -1 = -1.$

Stumbling Robot