$4.(2$ points$)$ A rival alien scientist named Faxe has come up with their own conversion process for turning water into orsh. Their process is described by the function

$\backslash [$

F$($P$)=\backslash$frac$\{$P$^\{3\}+10\}\{1+($P$-2)^\{2\}\}$

$\backslash ]$

$($a$)(1$ point$)$ We already know that Genly's processes have a high peak efficiency at a low pressure.

If the aliens are able to apply very high pressures $($much higher than the values of $\backslash ($ P$\_\{$b$\}\backslash )$ you were thinking about in Q$2$ and Q$3),$ which process would be produce more orsh per litre of water?

State your answer $("$Genly$"$ or "Faxe"$)$ at the top of your answer and, in at most two sentences and some short computations, justify your choice below.

$($b$)(1$ point$)$ Another alien named Tibe works in Faxe's laboratory and has experimented with Faxe's process at high pressures.

Tibe says that for very high pressures, the increase in orsh production per litre of water from Faxe's process is directly proportional to the increase in pressure $($i$.$e$.,$ Tibe believes that $\backslash ($ F $\backslash )$ is a line for large values of $\backslash ($ P $\backslash )).$ Faxe hears this and thinks this is at best a good approximation for what happens at high pressures. The two of them come to the MAT$135$ students, who have just learned about different types of asymptotes in class, for some clarification.

In at most a few sentences and some computations, explain which one of Faxe or Tibe is more correct about $\backslash ($ F $\backslash ),$ and why.