Question

Calcule o e marque a alternativa correta. Escolha uma: a. 4 b. -4 c. 1/4 d. -1/4 e. 6

Answer 1

Resposta:

$\begin{lgathered}\displaystyle\mathsf{ \frac{1}{4}} \end{lgathered}$

Explicação passo-a-passo:

$\begin{lgathered}\displaystyle\mathsf{\lim_{x \to -1}\dfrac{\sqrt{x+5}-2}{x+1}} \\ \\\displaystyle\mathsf{\lim_{x \to -1}\dfrac{(\sqrt{x+5}-2) ( \sqrt{x+5}+2)}{(x+1)(\sqrt{x+5}+2)}}\end{lgathered}$

$\begin{lgathered}\displaystyle\mathsf{\lim_{x \to -1}\dfrac{ \left ( \sqrt{x+5} \right )^2 - 2^2 }{(x+1)(\sqrt{x+5}+2)}} \\ \\ \displaystyle\mathsf{\lim_{x \to -1}\dfrac{x+5-4}{(x+1)(\sqrt{x+5}+2)}} \end{lgathered}$

$\begin{lgathered}\displaystyle\mathsf{\lim_{x \to -1}\dfrac{(x+1) }{(x+1)(\sqrt{x+5}+2)}} \\ \\ \displaystyle\mathsf{\lim_{x \to -1}\dfrac{1}{(\sqrt{x+5}+2)}} \end{lgathered}$

$\begin{lgathered}\displaystyle\mathsf{\lim_{x \to -1}\dfrac{1 }{(\sqrt{x+5}+2)}= \frac{1}{\sqrt{-1+5}+2 } = } \\ \\ \displaystyle\mathsf{ = \frac{1}{\sqrt{4}+2} = \frac{1}{2+2} = \frac{1}{4}} \end{lgathered}$