Question

Lim(((2-x)/(7-x))^(6x-7))
X-> +бесконечности

Answer 1

Ответ:

$\lim\limits _{x \to \infty}\Big(\dfrac{2-x}{7-x}\Big)^{6x-7}=\lim\limits _{x \to \infty}\Big(\dfrac{x-2}{x-7}\Big)^{6x-7}=\lim\limits _{x \to \infty}\left(\Big(1+\dfrac{5}{x-7}\Big)^{\dfrac{x-7}{5}}\right)^{\dfrac{5\, (6x-7)}{x-7}}=\\\\\\=e^{\lim\limits _{x \to \infty}\dfrac{30x-35}{x-7}}=e^{30}$