Question

lim
$\frac{ \sqrt{1 + x} - 1}{ - x}$
Com X tendendo a 0​

Answer 1

Resposta:

Explicação passo-a-passo:

Vamos multiplicar o numerador e o denominador por $\sqrt{1+x}+1$

$\lim_{x \to 0} \frac{(\sqrt{1+x}-1).(\sqrt{1+x}+1)}{-x.(\sqrt{1+x}+1)}=\\\\\\= \lim_{x \to 0} \frac{1+x-1}{-x.(\sqrt{1+x}+1)}=\\\\\\= \lim_{x \to 0} \frac{x}{-x.(\sqrt{1+x}+1)}=\\\\\\= \lim_{x \to 0} \frac{1}{-(\sqrt{1+x}+1)}=\\\\\\=\dfrac{1}{-(\sqrt{1+0}+1)}=\dfrac{1}{-(\sqrt{1}+1)}=\dfrac{1}{-(1+1)}=-\dfrac{1}{2}$