Consider the following. \[ g(x)=4 x \operatorname{sech}(x) \] Find \( g^{\prime}(x) \). \( g^{\prime}(x)=\square \) Find any critical numbers of \( g \). (Enter your answers as a comma-separated list. Round your answers to four decimal places.) Find the relative extrema of the function. (Round your answers to four decimal places.) relative maxima \( \quad(x, y)=(\square) \) relative minima \[ (x, y)=(\square) \]

\( \lim _ { m \rightarrow + \infty } m [ 2 - \sin ( n ^ { 2 } + 1 ) ] \)

8. \( \int \frac{8 x^{2} d x}{\left(x^{3}+9\right)^{3}} \)

Consider the following. \[ \begin{array}{l}y=x^{2} \\ y \\ y \\ y\end{array} \] (b) Use the integration capabilities of the graphing utility to approximate the area to four de

Soit \( f \) la fonction définle sur un domaine de dȩ̀inition par \( f(x)=\frac{1}{5}\left(-\sqrt{x} e^{-4 x}\right) \). On admettra que \( f \) est dérivable deux fois sur chaque intervalle contenu dans son domaine de définition. Donner la dérivée de \( f \).

8. \( \int \frac{8 x^{2} d x}{\left(x^{3}+2\right)^{3}} \)