Question

Lim (9-x)/(3-√x), x ->9. Correct answer is 6

Answer 1

$\lim_{x\to 9}\dfrac{9-x}{3-\sqrt x}=\\ \lim_{x\to 9}\dfrac{(9-x)'}{(3-\sqrt x)'}=\\ \lim_{x\to 9}\dfrac{-1}{-\dfrac{1}{2\sqrt x}}=\\ \lim_{x\to 9}2\sqrt x=\\ 2\sqrt9=\\ 2\cdot3=\\ 6$