Al calcular el \( \lim _{x \mapsto 0} \frac{2 x^{2}}{3-3 \cos x} \) se obtiene:

One measure of living standards in country \( A \) is given by the following formula \( L(t)=7+4 e^{0.14 t} \) In this formula \( t \) is the number of years since 1982. Find \( L \) to the nearest hund \( \begin{array}{ll}\text { (a) } 1988 & \text { (b)1998 } \\ \text { (c)2007 }\end{array} \) \( \begin{array}{l}\text { (a) Find } L \text { for } 1988 . \\ \text { (Round to the nearest hundredth as needed.) } \\ \text { (b) Find } L \text { for } 1998 . \\ L=\square\end{array} \) (Round to the nearest hundredth as needed.) (c) Find \( L \) for 2007 .

Encontrar \( f(t) \) si \( F(s)=\frac{2}{(s+2)^{4}}+\frac{3}{s^{2}+16}+\frac{5(s+1)}{s^{2}+2 s+5} \)

Determine la longitud de la curva \( x=\frac{y^{5}}{5}+\frac{1}{12 y^{3}} \) en el intervalo \( y \in[1,2] \). resultado con dos decimales.

Analizar en cada caso si es posible aplicar el Teorema de Stokes para calcular la circulación de \( \vec{F} \) a lo largo de \( C:\left\{\begin{array}{l}x^{2}+y^{2}=1 \\ z=0\end{array}\right. \) Hallar el valor de esa circulación. (i) \( \vec{F}=\left\langle\frac{-x}{\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2}}, \frac{-y}{\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2}}, \frac{-z}{\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2}}\right\rangle \)

Encontrar \( f(t) \) si \( \rho(s)=\frac{s}{s^{2}+6 s+10} \)