Evaluate the following limit related to square roots.

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Evaluate the following limit related to square roots. (i) Show that the expression

\dfrac{\sqrt{x+6}-\sqrt{9}}{x-3}

takes the indeterminate form

\dfrac{0}{0}

x\to3

. (ii) Hence find

\displaystyle \lim_{x\to3}\dfrac{\sqrt{x+6}-\sqrt{9}}{x-3}