Question

ajuda com limites? por favor o or!

Answer 1

Boa noite!

Solução!

$\displaystyle \lim_{x \to 0} \frac{ \sqrt{x+2} - \sqrt{2} }{x} \\\\\\\\ \displaystyle \lim_{x \to 0} \frac{ \sqrt{x+2} -\sqrt{2} }{x}\times \frac{ \sqrt{x+2}+ \sqrt{2} }{ \sqrt{x+2} + \sqrt{2} } \\\\\\\\ \displaystyle \lim_{x \to 0} \frac{ (\sqrt{x+2})^{2} + \sqrt{2}.\sqrt{x+2})- \sqrt{2} .\sqrt{x+2} - (\sqrt{2})^{2} }{x \sqrt{x+2}+ \sqrt{2} }$


$\displaystyle \lim_{x \to 0} \frac{x+2-2}{x \sqrt{x+2}+ \sqrt{2} }\\\\\\\ \displaystyle \lim_{x \to 0} \frac{x}{x \sqrt{x+2}+ \sqrt{2} }\\\\\\\ \displaystyle \lim_{x \to 0} \frac{1}{ \sqrt{x+2}+ \sqrt{2} }\\\\\\\\\ Substituindo~~zero!\\\\\\\\ \displaystyle \lim_{x \to 0} \frac{1}{ \sqrt{2}+ \sqrt{2}}\\\\\\\\\ \boxed{\displaystyle \lim_{x \to 0} \frac{1}{2 \sqrt{2}}}\\\\\\\\\ \displaystyle \lim_{x \to 0} \frac{2 \sqrt{2} }{2.2}}$


$\boxed{\displaystyle \lim_{x \to 0} \frac{\sqrt{2} }{2}}}$

Boa noite!
Bons estudos!