Recall the definitions of the asymptotic notations. We will say that f$($x$)$ has $$order of growth x

$\backslash$alpha

as x $->$ x$0($where x$0$ is either some fixed real number or $\backslash$pm $\backslash$infty $)$ if f$($x$)=\backslash$Theta $($x

$\backslash$alpha $)$ as x $->$ x$0.$

$1.$ Consider the functions f$($x$)=$ x sin x and g$($x$)=$ x$.$ Is f$($x$)=\backslash$Theta $($g$($x$))$ as x $->\backslash$infty $?$ Why or

why not? $($Hint: As always, you should refer back carefully to the definition of $\backslash$Theta $().)$