Dadala función \( y=f(x)=\frac{2}{x} \) Hallaref volumen del solido generado al 1 la region entre el eje \( y \) i 12 curva. \( x=\frac{2}{y} \) \( 1 \leq 4 \leq 4 \), alrededor del eje \( y \).

Use spherical coordinates to evaluate the triple integral \( \iiint_{E}\left(x^{2}+y^{2}+z^{2}\right) d V \) where \( E \) is the ball: \( x^{2}+y^{2}+z^{2} \leq 100 \).

Find the derivative of the following: \( y=x^{2} \cdot \ln x+\sqrt{x^{3}+2 x} \)

16. ( 3 points) The position of a particle on a line is given by \( s(t)=-3 t^{2}+6 t+5 \) where \( t \) is measured in seconds and \( s \) is measured in feet. Find the speed of the psrticle when \( t=2 \) seconds. \( \begin{array}{ll}\text { (A) }-6 \mathrm{ft} / \mathrm{s} & \text { (B) } 6 \mathrm{ft} / \mathrm{s} \\ \text { (C) }-1 \mathrm{ft} / \mathrm{s} & \text { (D) } 5 \mathrm{ft} / \mathrm{s}\end{array} \)

\( \int _{0}^{\frac{\pi }{2}}\int _{2\sin (\theta )}^{2}(r\cos (\theta )+r\sin (\theta ))r d r d \theta \)

16. ( 3 points) The position of a particle on a line is given by \( s(t)=-3 t^{2}+6 t+5 \) where \( t \) is measured in seconds and \( s \) is measured in feet. Find the speed of the particle when \( t=2 \) seconds. \( \begin{array}{ll}\text { A }-6 \mathrm{ft} / \mathrm{s} & \text { (B) } 6 \mathrm{ft} / \mathrm{s} \\ \text { (C) }-1 \mathrm{ft} / \mathrm{s} & \text { (D) } 5 \mathrm{ft} / \mathrm{s}\end{array} \)