Question

lim x-->5
√x-4 - √3x - 14
----------------------
       x-5

Answer 1

$\displaystyle L=\lim\limits_{x\to 5}\frac{\sqrt{x-4}-\sqrt{3x-14}}{x-5}\\ \\ \\ L=\lim\limits_{x\to 5}\frac{\sqrt{x-4}-\sqrt{3x-14}}{x-5}\times \frac{\sqrt{x-4}+\sqrt{3x-14}}{\sqrt{x-4}+\sqrt{3x-14}}\\ \\ \\ L=\lim\limits_{x\to 5}\frac{-2x+10}{(x-5)(\sqrt{x-4}+\sqrt{3x-14})}\\ \\ \\ L=\lim\limits_{x\to 5}\frac{-2}{\sqrt{x-4}+\sqrt{3x-14}}\\ \\ \\ \boxed{L=-1}$