Determine el volumen resultante de rotar la función \( f(x) = \frac{1}{x} \), desde \( x = 1 \) hasta \( x = 2 \), alrededor del eje y usando el método de lavadoras.

\( \frac{d}{dx}((x\times \sin (xy-y^{2})=x^{2}-1)) \)

\( \lim _ { n \rightarrow \infty } \frac { n \cdot \sin \frac { 1 } { n } - \cos \frac { 1 } { n } } { \ln ( 1 + \frac { 1 } { n ^ { 2 } } ) } \)

\( \frac{d}{dx}(x\times \sin (xy-y^{2})=x^{2}-1) \)

A solid is formed with triangular cross-sections where each triangle's base is defined by the equation \(y = x^2\) on interval \([0, 2]\). What is the volume of this solid?

Discur the convergene at \( [1,2] \) given that \( f(x)=x^{3}-x-1 \)