Calculate the volume of the solid formed by rotating the region bounded by the curve \( y = x^2 \) and the line \( y = 1 \) around the x-axis using the washer method.

\( \frac { d y } { d x } = 1 + x + y ^ { 2 } + x y \)

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

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

\( \lim _ { x \rightarrow r } \frac { x ^ { T } - 9 } { \sqrt { x + 1 } - 1 } = \)

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