Question

найти пределы...... .

Answer 1

$displaystyle lim_{n to infty} frac{n}{(n+3)^2}=lim_{n to infty} frac{n}{n^2+6n+9}=\=lim_{n to infty} frac{n:n}{n^2:n+6n:n+9:n}=lim_{n to infty} frac{1}{n+6+frac{9}{n}}=0;$

$displaystyle lim_{n to infty} frac{2+10n}{5n-1}=lim_{n to infty} frac{2:5n+10n:5n}{5n:5n-1:5n}=\lim_{n to infty} frac{frac{2}{5n}+2}{1-frac{1}{5n}}=frac{2}{1}=2$

$displaystyle lim_{n to infty} frac{4+n^3}{2n}=lim_{n to infty} frac{4:n+n^3:n}{2n:n}=\lim_{n to infty} frac{frac{4}{n}+n^2}{2}=infty$