Question

evaluate limit as x approaches 2 of (sqrt(6-x) -2)/(sqrt(3-x) - 1)

Answer 1

\[\lim_{x\to2}\frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}\]
You get the indeterminate form \(\dfrac{0}{0}\), so you can apply L'Hopital's rule directly.

I'm not sure if there's another analytical way to approach this, since rationalizing the numerator and denominator also gives you \(\dfrac{0}{0}\).