Êquations découplées. Résoudre les systèmes différentiels suivants \[ \left\{\begin{array}{l}x_{1}^{\prime}=-x_{1} \\ x_{2}^{\prime}=2 x_{2}\end{array}, \text { (b) }\left\{\begin{array}{l}x_{1}^{\prime}=-x_{1}+x_{2} \\ x_{2}^{\prime}=-x_{2}\end{array}\right.\right. \]

Find equations of the tangent line and normal line to \( x^{2}+4 x y+y^{2}=13,(2,1) \)

\( \lim _ { z - 1 } \frac { 4 z + 3 } { 2 z + 1 } \)

23-24 ¿Cómo podría "remover la discontinuidad" en cada una de las siguientes funciones? En otras palabras, ¿cómo redefiniría \( f(2) \) a fin de que sean continuas en \( x=2 \) ? \( \begin{array}{ll}\text { 23. } f(x)=\frac{x^{2}-x-2}{x-2} & \text { 24. } f(x)=\frac{x^{3}-8}{x^{2}-4}\end{array} \)

Find differenthal equation of the primitue \( x y+x^{2} y+y^{2}=13 \)

4. Let \( g \) be a function such that \( g(1)=3 \) and whose derivative is \( g^{\prime}(x)=6 \cos (2 \pi x)+3 \). Solve analytically a. Use a linear approximation to estimate the value of \( g(1.2) \). b. Find the solution to the differential equation \( d g=(6 \cos (2 \pi x)+3) d x \)