sider the function \( f \) defined over \( ]-\infty ; 0[\mathrm{U}] 0 ;+\infty\left[\right. \) by \( f(x)=\frac{x^{3}+x^{2}-x-1}{x^{2}} \) and let (C) b fresentative curve in an orthonormal system \( (O ; \vec{\imath}, \vec{\jmath}] \). Find the limits of \( f \) at the boundaries of its domain. Deduce the equation of an asympto Show that \( f \) can be written as \( f(x)=x+1-\frac{x+1}{x^{2}} \). Show that the line (D): \( y=x+1 \) is an oblique asymptote to (C).

\( y ^ { \prime \prime } - y ^ { \prime } - 2 y = x e ^ { 2 u } - e ^ { 2 u } \sin ( 2 x ) \)

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.

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. \[ g(x)=9 x+\frac{1}{x} \]

find the easiest solution, please: 1) \( \frac{\lim }{12} \frac{x^{5} \sqrt[3]{x+6}-64}{x-2}= \)

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