3)- Si el \( \lim _{x \rightarrow a^{-}} f(x)=-\infty \) y \( \lim _{x \rightarrow a^{+}} f(x) \exists \), centonces \( \lim _{x \rightarrow a} f(x) \exists \) ?. Da ejemplos graticos. 4)- Calcula la continuidad, o no, de la función: \( f(x)=\frac{\operatorname{sen} x}{x} \) en \( x=0 \)

La derivada de \( e^{x^{2}+2 x+2} \) es: A) \( (2 x-2) e^{x^{2}+2 x+2} \) B) \( (2+2) e^{x^{2}+2 x+2} \) C) \( (2 x+2) e^{x^{2}+2 x+2} \) D) \( -(2 x+2) e^{x^{2}+2 x+2} \)

importante de l'appréciation des copies. Les résultats doivent être encadrés. L'usage de la calculatrice n'est pas autorisé au cours de l'épreuve. Exercice 1. \( \quad \) 1. Étudier la nature des séries suivantes : (a) \( \sum_{n} \frac{n}{2 n^{3}+1} ; \sum_{n} \frac{\ln ^{3}(n)}{n^{2}} ; \sum_{n} \frac{\ln (n+1)}{n \sqrt{n+1}} ; \sum_{n} \sqrt{n} e^{-n^{2}} ; \sum_{n} \ln (n) e^{-n} \).

Let \( R \) be the region enclosed by the graphs of \( f(x)=4 \cos (x)-1 \) and \( g(x)=4 \sin (x)-2 \). Find the length of the boundary of region \( R \). Use a calculator and round your answer to 3 decimal places.

17. La fintegralde \( \int 3 e^{3 x} d x=e s: \) \( \begin{array}{ll}\text { a) } \frac{e^{3 x}}{-2}+c & \text { b) } \frac{3}{-x}+c \\ \text { c) } e^{3 x}+c & \text { d) } \frac{x e^{-2}}{-2}+c\end{array} \)

Find the producers' surplus at a price level of \( \overline{\mathrm{p}}=\$ 64 \) for the price-supply equation below. \( \mathrm{p}=\mathrm{S}(\mathrm{x})=15+0.1 x+0.0003 \mathrm{x}^{2} \) The producers' surplus is \( \$ \square \). (Round to the nearest integer as needed.)