Question $2.$ Asymptotics

Another common approximation in applied math and engineering is to use only the leading order terms for functions that grow without bound. In this exercise we will recall how to use the $$big$-$O$$ notation to denote such an

approximation, and write some simple MATLAB code that can help us confirm when the definition can be applied.

$($a$)$ Consider the functions

f$1($x$)=$ e

x

$,$

and

f$2($x$)=$ e

$($x

$2$

$)$

$.$

Is it true that f$1($x$)$ in O$($f$2($x$))$ or that f$2($x$)$ in O$($f$1($x$))$ as x $->\backslash$infty $?$ Justify your answer by taking a limit$.$