\( \sum _ { n = 1 } ^ { \infty } \frac { 2 ^ { n } \operatorname { Ln } ( n ) } { ( 1,3 ) ^ { n } } \)

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) \( a^{n} e^{a x} \)

Calculate the area enclosed between the lines \( y = 2x + 3 \) and \( y = x^2 \).

Sol. Solve same as Q. No. 40 (a). Q. 41. Find all asymptotes of the curve \( x^{3}+y^{3}=3 \) axy. \[ \text { (Bhopal 1991, } 2000 \]

Answer any THREE. \( \lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{1}{\ln x}\right) \)

(Q6; 2,6 балла) Найдите наименьшее значение выражения \( 16 x+\frac{9}{25 x}(x>0) \), используя \( \frac{a+b}{2} \geq \sqrt{a b} \).