Question

alguem consegue resolver esse limite lim┬(n→5)⁡〖(x-5)/(√(20+x)-5)〗

Answer 1

$\lim_{x \rightarrow 5} \frac{x - 5}{\sqrt{20 + x} - 5} = \\\\\\ \lim_{x \rightarrow 5} \frac{x - 5}{\sqrt{20 + x} - 5} \times \frac{\sqrt{20 + x} + 5}{\sqrt{20 + x} + 5} = \\\\\\ \lim_{x \rightarrow 5} \frac{(x - 5)(\sqrt{20 + x} + 5)}{20 + x - 25} = \\\\\\ \lim_{x \rightarrow 5} \frac{(x - 5)(\sqrt{20 + x} + 5)}{x - 5} = \\\\\\ \lim_{x \rightarrow 5} \sqrt{20 + x} + 5 = \\\\ \lim_{x \rightarrow 5} \sqrt{20 + 5} + 5 = \\\\ \sqrt{25} + 5 = \\\\ \boxed{10}$