Question

por favorr... calcule o limite raiz 5+y - raiz 5 / y quando y=0

Answer 1

$\lim\limits_{y\to0}\dfrac{\sqrt{5+y}-\sqrt{5}}{y}=\lim\limits_{y\to0}\left(\dfrac{\sqrt{5+y}-\sqrt{5}}{y}\times\dfrac{\sqrt{5+y}+\sqrt{5}}{\sqrt{5+y}+\sqrt{5}}\right)=\\\\\\=\lim\limits_{y\to0}\dfrac{5+y+\sqrt{25+5y}-\sqrt{25+5y}-5}{y(\sqrt{5+y}+\sqrt{5})}=\lim\limits_{y\to0}\dfrac{y}{y(\sqrt{5+y}+\sqrt{5})}=\\\\\\=\lim\limits_{y\to0}\dfrac{1}{\sqrt{5+y}+\sqrt{5}}=\dfrac{1}{\sqrt{5+0}+\sqrt{5}}=\dfrac{1}{2\sqrt{5}}=\bold{\dfrac{\sqrt{5}}{10}}$