77-78 Use l'Hospital's Rule to evaluate the limit. 77. \( \lim _{x \rightarrow 0} \frac{1}{x^{2}} \int_{0}^{x} \frac{2 t}{\sqrt{t^{3}+1}} d t \)

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

Find an equation of the tangent plane to the given parametric surface at the specifie point. \( \begin{array}{l}\text { (a) } r(u, v)=\left(u^{2}+1\right) \mathbf{i}+\left(v^{3}+1\right) \mathbf{j}+(u+v) \mathbf{k} .(5,2,3) \\ \text { (b) } r(u, v)=\sin u \mathbf{i}+\cos u \sin v \mathbf{j}+\sin v \mathbf{k},(0.5, \sqrt{3} / 4,0.5)\end{array} \)

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

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

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