If \( \frac{d^{n t}}{d x^{n}}\left(e^{a x}\right)=\quad \) where \( a, b \) are constar (ii) \( a^{n-1} e^{a x} \) (iii) \( n!a^{n} \) (iii) \( (n-1)!a^{n-1} \) (iv) \( a^{n} e^{a x} \)

If a car has an acceleration function of \( a(t) = 6t \), what is its velocity function assuming it starts from rest?

(j.) \( y=\ln \sqrt{\frac{2}{x^{3}}} \)

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

(d.) \( f(x)=\left(\frac{x+5}{x^{2}+2}\right)^{2} \)

If \( \left\langle a_{n}\right\rangle \) and \( \left\langle b_{n}\right\rangle \) are two sequences such that \( \lim _{n \rightarrow \infty} a_{n}=i, \lim _{n \rightarrow \infty} b_{n}=m \), then prove that: \( \lim _{n \rightarrow \infty}\left(a_{n}+b_{n}\right)=l+m \)