Giải thích các bước giải:
2. \(lim \frac{(n^{2}-n-1)^{2}(3-n)^{3}}{(n+2)^{5}(n^{2}-5n-3)}=lim \frac{(\frac{n^{2}-n-1}{n^{2}})^{2}(\frac{3-n}{n})^{3}}{(\frac{n+2}{n})^{5}.\frac{n^{2}-5n-3}{n^{2}}}=lim \frac{(1-\frac{1}{n}-\frac{1}{n^{2}})^{2}(\frac{3}{n}-1)^{3}}{(1+\frac{2}{n})^{5}(1-\frac{5}{n}-\frac{3}{n^{2}})}=-1\)
3. \(lim \frac{n^{3}-4n-3}{(2n^{2}-n-1)^{2}}=lim \frac{\frac{1}{n}-\frac{4}{n^{3}}-\frac{3}{n^{4}}}{(2-\frac{1}{n}-\frac{1}{n^{2}})^{2}}=lim \frac{0}{2}=0\)
4. \(+\infty\) (chia tử mẫu cho \(n^{3}\))
5. \(lim \frac{\sqrt{n^{2}-n}+2n-1}{\sqrt[3]{n^{3}-5n-2}-4n+1}=lim \frac{\sqrt{1-\frac{1}{n}}+2-\frac{1}{n}}{\sqrt[3]{1-\frac{5}{n^{2}}-\frac{2}{n^{3}}}-4+\frac{1}{n}}=lim -1=-1\)
