Question

lim x - 16 dividido por raiz quarta de x - 2
x tendendo a 16

Answer 1

$\lim_{x \to \116} \frac{x-16}{ \sqrt[4]{x}-2 }$

Fazendo x = t⁴ ; x →16 ⇒ t→2

$\lim_{x \to \16} \frac{x-16}{ \sqrt[4]{x} -2} = \lim_{t \to \22} \frac{t ^{4}-16 }{ \sqrt[4]{t ^{4} } -2} = \lim_{t \to \22} \frac{(t^2+4)(t^2-4)}{t-2} = \\ \\ \lim_{t \to \22} \frac{(t^2+4)(t+2)(t-2)}{t-2} = \lim_{t \to \22} (t^2+4)(t+2) = (2^2+4)(2+2)= \\ \\ =8.4=32$