\( \frac { n ! } { ( n + 1 ) ^ { n } } = \)

encuentre el volumen del sólido aco- tado por las gráficas de las ecuaciones dadas. \( r=1+\cos \theta, z=y, z=0 \)

\( \left. \begin{array} { l } { f ^ { \prime } ( x ) = } \\ { f ( x ) = \sqrt { \cos ( e ^ { x ^ { 5 } \sin ( x ) } ) } } \\ { \frac { 5 x ^ { 4 } e ^ { x ^ { 5 } \cdot \sin ( x ) } \cdot - \sin ( e ^ { x ^ { 5 } \cdot \sin ( x ) } ) \cdot - \sin ( x ) - x ^ { 5 } e ^ { x ^ { 5 } \cdot \sin ( x ) } \cdot \sin ( e ^ { x ^ { 5 } \cdot \sin ( x ) } ) \cos ( x ) } { 2 \sqrt { \cos ( e ^ { x ^ { 5 } \sin ( x ) } ) } } } \end{array} \right. \)

derivates \( y=\frac{1+x^{3}}{1-x^{3}} \)

(f) \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\cos x}{1-\tan x} \) (g) \( \lim _{x \rightarrow 0} \frac{x-\sin 2 x}{x+\sin 3 x} \) (h) \( \lim _{x \rightarrow 0} \frac{1-\sqrt{\cos x}}{x^{2}} \) (i) \( \lim _{x \rightarrow \infty}\left(\frac{x-1}{x+3}\right)^{x+2} \)

CHECKING COMPREMENSION (press pause for more time) Find the volume of the solid of revolution that results from rotating \( y=x^{2}+3 \) around the \( x \) axis, over the interval from 0 to 1 .