Question

ayudenme con el limite de x cuando tiende a 4, de 3-[raiz de (5+x)] / 1-[raiz de (5-x)]

Answer 1

$<var> \\\lim_{x\to4}\frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}=\\ \lim_{x\to4}\frac{(3-\sqrt{5+x})'}{(1-\sqrt{5-x})'}=\\ \lim_{x\to4}\frac{-\frac{1}{\sqrt{5+x}}\cdot1}{-\frac{1}{\sqrt{5-x}}\cdot(-1)}=\\ \lim_{x\to4}-\frac{\sqrt{5-x}}{\sqrt{5+x}}=\\ -\frac{\sqrt{5-4}}{\sqrt{5+4}}=\\ -\frac{\sqrt1}{\sqrt9}=\\ -\frac{1}{3}</var>$