Question

Calcule limites
lim [(2+T)^4 - 16 / T]
T -> 0

Answer 1

$\lim_{t \to \00} \frac{(t +2)^4-16}{t}= \lim_{u \to \22} \frac{u^4-16}{u-2} = \lim_{u \to \22} \frac{(u^2+4)(u^2-4)}{u-2} = \\ \\ \lim_{u \to \22} \frac{(u^2+4)(u-2)(u+2)}{u-2} = \lim_{u \to \22} (u^2+4)(u+2)=(2^2+4)(2+2)= \\ \\ =(4+4).4=8.4=32$

Cálculos auxiliares: fazendo t + 2 = u ⇒ t = u - 2  ; t →0 ⇒ u →2