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 the limit is taken as $x$ approaches zero through positive 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