\begin{tabular}{l} Question \\ Evaluate the following limit using L'Hospital's rule. \\ \( \qquad \)\begin{tabular}{l}\( \lim _{x \rightarrow 0} \frac{7 \sin (5 x)}{2 \tan (2 x)} \) \\ Enter an exact answer. \\ \( \qquad \begin{array}{l}\lim _{x \rightarrow 0} \frac{7 \sin (5 x)}{2 \tan (2 x)}=\square\end{array} \) \\ \hline\end{tabular}. \\ \hline\end{tabular}

Soit \( f \) la fonction définie sur \( \mathbb{R}^{+} \operatorname{par} f(x)=\frac{2 \sqrt{x}}{x+1} \) Monter que \( f \) est majoréeqar 1. \( f \) est-elle bornée? Justifier votre réponse.

\( F ( x ) = \int _ { x } ^ { x ^ { 2 } } e ^ { t ^ { 7 } } d t \)

\( f : R ^ { 2 } \rightarrow R , f ( x , y ) = 2 x ^ { 2 } + 3 x y + 4 y ^ { 2 } - 5 x + 2 y + 2024 \)

find the easiest solution, please: 1) \( \frac{\lim _{2}}{\frac{x^{5}}{\sqrt[3]{x+6}-64}} x \)

7 Determina os intervalos de monotonia da função \( g \) a seguir definida, em \( \mathbb{R} \backslash\{0\} \), e iden- tifica os extremos relativos e absolutos, caso existam. \[ g(x)=9 x+\frac{1}{x} \]