Consider the following equations. \[ \begin{array}{l}f(x)=\sqrt{x}+6 \\ g(x)=\frac{1}{4} x+6\end{array} \] Sketch the region bounded by the graphs of the functions. Find the area of the region.

Calcolare il limite \( \lim _{x \rightarrow+\infty} x \log \left(1-\frac{1}{x}\right) \) amente all'esercizio 8.18 , si trova il valore limite -1\( ] \)

\( \sum _ { 0 } ^ { \infty } ( - 7 ) ^ { n } x ^ { 4 n + 2 } \)

\( f(x, y, z)=\left(x^{2} y z+x y^{2} z+x y z^{2}\right)^{2} \) function. \( \begin{array}{l}\text { (a) Find } \frac{\partial f}{\partial y} \quad(5 \mathrm{pts}) \\ \text { (b) Find } \frac{\partial^{2} f}{\partial y^{2}} \quad(5 \mathrm{pts}) \\ \text { (c) The value of } \frac{\partial f}{\partial y} \text { for } \mathrm{x}=2, \mathrm{y}=-1 \\ \text { and } \mathrm{z}=0 \quad(5 \mathrm{pts})\end{array} \)

\( \lim _ { x \rightarrow - \infty } ( 2 - x ) \sin \frac { 1 } { x } \)

\( f(x, y, z)=\left(x^{2} y z+x y^{2} z+x y z^{2}\right)^{2} \) (a) Find \( \frac{\partial f}{\partial y} \quad(5 \mathrm{pts}) \)