Question

Calculando o limite de lim x -> 0 (√(5+x) - √5) / x obtemos:

Answer 1

lim x->0 (raiz(5+x) - raiz(5))/x

lim x->0 (y)

$y=\frac{\sqrt{5+x} -\sqrt{5} }{x} *\frac{\sqrt{5+x} +\sqrt{5} }{\sqrt{5+x} +\sqrt{5} } \\y=\frac{5+x-5}{x*(\sqrt{5+x} +\sqrt{5} )} \\y=\frac{x}{x*(\sqrt{5+x} +\sqrt{5} )} \\y=\frac{1}{(\sqrt{5+x} +\sqrt{5} )}$

lim x-> 0 $\frac{1}{(\sqrt{5+x} +\sqrt{5} )}$  = $\frac{1}{2\sqrt{5} }$