Question

Quero saber o limite.
Eu sei que substituindo vai da 0
Quero passo a passo a resposta, por favor.

$\lim_{x \to \-2} \frac{\sqrt{x}-\sqrt{2} }{x-2}$

Answer 1

Resposta:

$\boxed{\lim_{x \to 2} \dfrac{\sqrt{x}-\sqrt{2}}{x-2}=\dfrac{1}{2.\sqrt{2}}}$

Explicação passo-a-passo:

racionalizando o denominador

$\lim_{x \to 2}\dfrac{(\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2})}{(x-2)(\sqrt{x}+\sqrt{2})}=\\\\\\=\lim_{x \to 2}\dfrac{(x-2)}{(x-2)(\sqrt{x}+\sqrt{2})}=\\\\\\=\lim_{x \to 2}\dfrac{1}{\sqrt{x}+\sqrt{2}}=\\\\\\=\dfrac{1}{\sqrt{2}+\sqrt{2}}=\\\\\\=\dfrac{1}{2.\sqrt{2}}$

$\boxed{\lim_{x \to 2} \dfrac{\sqrt{x}-\sqrt{2}}{x-2}=\dfrac{1}{2.\sqrt{2}}}$