(x) \( \frac{y}{x} \frac{d y}{d x}=\frac{e^{x}}{\ln y} \)

Calculate the area bounded by the curves \( y = \sin(x) \) and \( y = \cos(x) \) over the interval \([0, \frac{\pi}{4}]\).

Determine the area bounded by the functions \( y = \sin(x) \) and \( y = \cos(x) \) within the interval \( [0, \frac{\pi}{2}] \).

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

d) \( \lim _{x \rightarrow 1} \frac{\ln x}{x^{2}-1}= \)

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