2. (3 points) If \( x \in[0, \pi] \), at which does the function \( y=\pi^{2}-\sin (x) \) have horizontal tangent lines? \( \begin{array}{ll}\text { (A) } x=\frac{\pi}{4} & \text { (B) } x=\frac{\pi}{6} \\ \text { (C) } x=\frac{\pi}{2} & \text { (D) } x=0, \pi\end{array} \)

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

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

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

Evaluate the line integral \( \int_{C} \mathbf{F} \cdot d \mathbf{r} \), where \( \mathbf{F}(x, y, z)=5 \sin (x) \mathbf{i}-4 \cos (y) \mathbf{j}-2 x z \mathbf{k} \) and C is given by the vector function \( \mathbf{r}(t)=t^{5} \mathbf{i}-t^{4} \mathbf{j}+t^{3} \mathbf{k}, \quad 0 \leq t \leq 1 \).

Ex. \[ \text { Let } f(x)=13 x-6 . \text { Find } f^{\prime}(\mathbf{4}) \]