Calculate the Riemann sum for the function \( f(x) = x^2 \) on the interval [1, 3] using 4 subintervals with left endpoints.

Find \( D_{x} y \) if \( y=\left(\frac{2}{x^{4}+1}+\frac{3}{x}\right) \)

Analyse Complexe 6. Trouvez les résidus en tout pôle des fonctions: a. \( f(z)=\frac{z^{2}-2 z}{(z+1)^{2}\left(z^{2}+4\right)} \)

1. Calcula la siguiente integral definio \( \int_{0}^{\pi} \sin (x) d x \)

\( \frac{d}{dx}(x^{2}+lnx-e^{3x)}) \)

9. Determinar la solución general del sistema: \[ \left\{\begin{array}{c}x_{1}^{\prime}=3 x_{1}+x_{2} \\ x_{2}^{\prime}=2 x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime}=2 x_{2}+3 x_{3}\end{array}\right. \]