2. \( y=\left(\frac{1+x^{2}}{1+x}\right)^{5} \)

The minimum value of the function \( f(x)=\frac{x}{x+1} \) is

The motion of a particle pertorming damped vibrations s given by \( \gamma=e^{-t} \operatorname{Sin} 2 t, \gamma \) being the displacement rom its mean position at time \( t \). Show that \( \gamma \) is a maximum when \( t=\frac{1}{2} \tan ^{-1}(2) \) and determine this maximum displacement to hree significant tigures.

The motion of a particle performing damped vibrations is given by \( \gamma=e^{-t} \sin 2 t, \gamma \) being the displacement trom its mean position at time \( t \). Show that \( \gamma \) is a maximum when \( t=\frac{1}{2 \tan ^{-1}(2)} \) and determine this maximum displacement to three significant figures.

\begin{tabular}{|l|}\hline Enunciado \\ \hline Determine si los siguientes enunciados son verdaderos \( (V) \) o faso \( (F) \) : \\ a. Si \( f(x)=3 x^{3}+6 \) cuando \( x \) varia de -3 a 1 su incremento es -24 \\ b. Si \( f(x)=3 x-2 \) cuando \( x \) varia de 2 a 2.5 no es un ejemplo de decremento \\ \hline\end{tabular}

Determina expresau a. \( \int 8 x\left(4 x^{2}-3\right) \) b. \( \int 2 t^{-3}\left(4 t^{-2}\right)^{-} \) c. \( \int_{1}^{3}\left(8 x-2 x^{2}\right) \)