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