\( \lim _ { n \rightarrow + \infty } \frac { n ! - ( n + 1 ) ! } { n ^ { 2 } e ^ { n } } = \)

\( \lim _ { n \rightarrow \infty } [ \frac { 1 } { \sqrt { 4 n ^ { 2 } - 1 } } + \frac { 1 } { \sqrt { 4 n ^ { 2 } - 2 ^ { 2 } } } + \cdots + \frac { 1 } { \sqrt { 3 n ^ { 2 } } } ] \)

Find differenthal equation of the primitue \( x y+x^{2} y+y^{2}=13 \)

(d) \( \lim _{n \rightarrow+\infty} \frac{\operatorname{sen}(1 / n)}{\operatorname{sen}(3 / n)} \)

Find the following indefinite integral \[ \int 9 x^{2} d x \]

\( \lim _ { m \rightarrow + \infty } \frac { t ^ { 2 } ( 1 | n ) } { 1 - \cos ( 1 / m ) } \)