Question

найти предел функции lim(3x-8)^2(х-3) при х стремящемся к 3

Answer 1

$\lim_{x \to 3}(3x-8)^{2(x-3)}=\lim_{x \to 3}(1+3(x-3))^{2(x-3)} = \\ =\lim_{t \to 0}(1+3t)^{2t}=\lim_{t \to 0}((1+3t)^{-3t})^{-\frac{2}{3}} = e^{-\frac{2}{3}} = \frac{1}{\sqrt[3]{e^2}}$