giải chi tiết cho mình với

`a)`

`lim \frac{2n + 1}{2 + n - n^{2}}`

`= lim \frac{\frac{2}{n} + \frac{1}{n^{2}}}{\frac{2}{n^{2}} + \frac{1}{n} - 1}`

`= \frac{0 + 0}{0 + 0 - 1}`

`= 0`

`b)`

`lim \frac{3 - \frac{2}{n}}{1 + \frac{3}{n}}`

`= \frac{3 - 0}{1 + 0}`

`= 3`

`c)`

`lim \frac{1 - 2n}{3n + 1}`

`= lim \frac{\frac{1}{n} - 2}{3 + \frac{1}{n}}`

`= \frac{0 - 2}{3 + 0}`

`= - \frac{2}{3}`

`d)`

`lim \frac{2n + 2024}{3n + 2025}`

`= lim \frac{2 + \frac{2024}{n}}{3 + \frac{2025}{n}}`

`= \frac{2 + 0}{3 + 0}`

`= \frac{2}{3}`

`e)`

`lim \frac{n^{2} - 3n^{3}}{2n^{3} + 5n - 2}`

`= lim \frac{\frac{1}{n} - 3}{2 + \frac{5}{n^{2}} - \frac{2}{n^{2}}}`

`= \frac{0 - 3}{2 + 0 - 0}`

`= - \frac{3}{2}`

`f)`

`lim \frac{10n + 3n^{3}}{3n - 15}`

`= lim \frac{\frac{10}{n^{2}} + 3}{\frac{3}{n^{2}} - \frac{15}{n^{3}}}`

`= + oo`

Vì `{(lim (\frac{10}{n^{2}} + 3) = 3 > 0),(lim (\frac{3}{n^{2}} - \frac{15}{n^{3}}) = 0):}`

$\color{pink}{\text{$\textit{$\circ$ hungnguyen4269}$}}$