Question

Найти предел lim
Подробно! Заранее спасибо!​

Answer 1

$lim_{n to infty} (frac{n^3}{n^2+1} - frac {3n^2}{3n-1} ) = (infty - infty) =  lim_{n to infty} {frac{n^3(3n-1)-3n^2(n^2+1)}{(n^2-1)(3n-1)}} =  lim_{n to infty} frac{3n^4-n^3-3n^4-3n^2}{3n^3-n^2+3n-1} =  lim_{n to infty} frac{-n^3-3n^2}{3n^3-n^2+3n-1} = -frac{1}{3}$