Question

Tá meio confuso isso aqui$\lim_{x \to \inft14} \frac{\sqrt{x+2}-4 }{x-14} _$

Answer 1

Resposta:

Explicação passo-a-passo:

Multiplique o numerador e denominador pelo conjugado do numerador

$\lim_{x\to14}\dfrac{\sqrt{x+2}-4}{x-14}=\\\\=\lim_{x\to14}\dfrac{\sqrt{x+2}-4}{x-14}.\dfrac{\sqrt{x+2}+4}{\sqrt{x+2}+4}=\\\\\\=\lim_{x\to14}\dfrac{x+2-16}{(x-14).(\sqrt{x+2}+4)}=\\\\\\=\lim_{x\to14}\dfrac{(x-14)}{(x-14).(\sqrt{x+2}+4)}=\\\\\\=\lim_{x\to14}\dfrac{1}{\sqrt{x+2}+4}=\dfrac{1}{\sqrt{14+2}+4}=\dfrac{1}{\sqrt{16}+4}=\\\\\\=\dfrac{1}{4+4}=\dfrac{1}{8}$