Obliczyć granicę ciągu: [latex] lim_{n o infty} sqrt[]{2 n^{2} +3n } - sqrt[]{2n} [/latex]                       [∞-∞]  korzystający z takiego wzoru: [latex]a-b= frac{ a^{2} - b^{2} }{a+b} [/latex]

[latex]displaystyle lim_{x o infty}sqrt{2n^2+3n}-sqrt{2n}=\\ lim_{x o infty}dfrac{2n^2+3n-2n}{sqrt{2n^2+3n}+sqrt{2n}}=\\ lim_{x o infty}dfrac{2n^2+n}{sqrt{n^2left(2+dfrac{1}{n} ight)}+sqrt{n^2left( dfrac{2}{n} ight)}}=\\ lim_{x o infty}dfrac{n(2n+1)}{nsqrt{2+dfrac{1}{n}}+nsqrt{ dfrac{2}{n}}}=\\ lim_{x o infty}dfrac{2n+1}{sqrt{2+dfrac{1}{n}}+sqrt{ dfrac{2}{n}}}=\\ dfrac{infty}{sqrt2+0}=\\ infty[/latex]