8) Find the volume of the solid formed by revolving the region bounded by the graph of the functions: \( y=\sqrt{x}, y=1 \) and \( x=0 \), around the \( x \)-axis. \( \begin{array}{llll}\frac{\pi}{2} & \text { (B) } \frac{\pi}{3} & \text { (C) } \frac{\pi}{4} & \text { (D) } \frac{\pi}{6}\end{array} \)

\( \int ^ { 3 A 3 } ( 3 ^ { x } - 3 ^ { 2 } ) : 3 + 3 ^ { 3 } : 3 ^ { 2 } = \)

Find the exact area of the resulting surface obtained by rotating about the y-axis the curve: \( y=\frac{1}{3} x^{\frac{3}{2}}, 0 \leq x \leq 12 \).

Find the exact area of the surface obtained by rotating about the \( x \)-axis the curve: \( x=\frac{1}{3}\left(y^{2}+2\right)^{\frac{3}{2}}, 1 \leq y \leq 2 \).

Find \( \frac{d^{2} y}{d x^{2}} \) given that \( x^{3}-3 x y+y^{3}=1 \)

If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( 1.2 .2 \quad f(x) \) non real. \( 1.2 .3 \quad f(x) \) undefined \( 1.2 .4 \quad f(x)>0 \) Simplify: \( \quad \frac{2^{x}-2^{-x}}{4^{x}-1} \)