18.
\(=lim\frac{\sqrt{1+\frac{2}{n}}}{1-\sqrt{3+\frac{1}{n^2}}}=\frac{1}{1-\sqrt{3}}\)
19.
\(=lim\frac{n\left(\sqrt{1+\frac{1}{n^2}}-\sqrt[3]{3+\frac{2}{n^3}}\right)}{n\sqrt[4]{2+\frac{2}{n^4}}}=lim\frac{\sqrt{1+\frac{1}{n^2}}-\sqrt[3]{3+\frac{2}{n^3}}}{\sqrt[4]{2+\frac{2}{n^4}}}=\frac{1-\sqrt[3]{3}}{\sqrt[4]{2}}\)
24.
\(=lim\frac{n\left(\sqrt[4]{1-\frac{2}{n^3}+\frac{1}{n^4}}+2\right)}{n\left(\sqrt[3]{3+\frac{1}{n^2}}-1\right)}=lim\frac{\sqrt[4]{1-\frac{2}{n^3}+\frac{1}{n^4}}+2}{\sqrt[3]{3+\frac{1}{n^2}}-1}=\frac{1+2}{\sqrt[3]{3}-1}=\frac{3}{\sqrt[3]{3}-1}\)
