Question

Помогите пожалуйста решить 13 задание

Answer 1

$1); ; limlimits _{n to infty} frac{2n+3}{3n-4} =Big [ frac{:n}{:n} Big ]= limlimits _{n to infty} frac{2+frac{3}{n}}{3-frac{4}{n}}=frac{2}{3} \\2); ; limlimits _{n to infty} frac{n-3n^2+44}{6n^2-3n+7}=Big [frac{:n^2}{:n^2} Big ] =limlimits _{n to infty} frac{-3+frac{1}{n}+frac{44}{n^2}}{6-frac{3}{n}+frac{7}{n^2}} = frac{-3}{6} = -frac{1}{2}$

$3); ; limlimits _{n to infty}frac{sin(n+3)}{n+3} =\\=Big [-1 leq sin(n+3) leq 1; -ogranichennaya ; ,; n+3to infty Big ]=0$

$4); ; limlimits _{n to infty} frac{1+2+...+n}{n^2} =\\=Big [1+2+...+n=frac{1+n}{2}cdot n=frac{n(n+1)}{2}; -; arifmet.progressiyaBig ]=\\= limlimits _{n to infty} frac{n(n+1)}{2n^2} = limlimits _{n to infty} frac{n^2+n}{2n^2}=Big [frac{:n^2}{:n^2} Big ]= limlimits _{n to infty} frac{1+frac{1}{n}}{2} =frac{1}{2}$