Question

Помогите!!!! $\lim_{n \to \infty} (\frac{2x+3}{5x+7})^{\frac{2x-1}{x-2}$

Answer 1

$\lim_{x \to \: \infty}( \frac{2x + 3}{5x + 7} )^{ \frac{2x - 1}{x - 2} } = \lim_{x \to \: \infty}( \frac{2x + 3}{5x + 7} )^ {\lim_{x \to \: \infty}( \frac{2x - 1}{x - 2} )} = \\ = \lim_{x \to \: \infty}( \frac{x(2 + \frac{3}{x}) }{x(5 + \frac{7}{x}) } )^{ \lim_{x \to \: \infty}( \frac{x(2 - \frac{1}{x} }{x(1 - \frac{2}{x}) } )} = (\frac{2 + \frac{3}{ \infty } }{5 + \frac{7}{ \infty } } )^{ \frac{2 - \frac{1}{ \infty } }{1 - \frac{2}{ \infty } } } = \\ = ( \frac{2}{5} )^{2} = \frac{4}{25} = 0.16$

Ответ: 0,16