Question

$lim_{x to infty} ( frac{3x}{3x+2})^{x+5}$

Answer 1

Решение смотрите в приложении.......

Answer 2

не одного пояснения даже(

Answer 3

$lim_{x to infty} ( frac{3x}{3x+2})^x^+^5= lim_{x to infty} 3^x^+^5( frac{x}{3x+2})^x^+^5= \ lim_{x to infty} exp(log(3)(x+5)+log( frac{x}{3x+2})(x+5))= \ exp( lim_{x to infty} (log(3)(x+5)+log( frac{x}{3x+2})(x+5))= \ exp( lim_{x to infty} log(3^x^+^5exp((x+5)(log(x)-log(3x+2))))=e^-^ frac{2}{3}= frac{1}{e^ frac{2}{3} }$