Calculate the limit $($as x goes to $4)$ of f$($x$)=3-2$x$,$ using our basic definitions of limits$.$The limit $($as x approaches p$)$ of the function f$($x$)$ is equal to L$$ means

$($Def$.6\mathrm{.}1)$ For all $\backslash$epsi $>0,$ there exists a $\backslash$delta $>0$ such that if x in D and $0<|$x$-$p$|<\backslash$delta $,$ then $|$f$($x$)-$L$|<\backslash$epsi $.$

$($Def$.6\mathrm{.}2)$ For all $\backslash$epsi $>0,$ there exists a $\backslash$delta $>0$ such that whenever x in N$\backslash$delta $*($p$)\backslash$cap D$,$ it follows that f$($x$)$ in N$\backslash$epsi $($L$).$

$($Def$.6\mathrm{.}3)$ For all $\backslash$epsi $>0,$ there exists a $\backslash$delta $>0$ such that the image of N$\backslash$delta $*($p$)\backslash$cap D is subset of N$\backslash$epsi $($L$).$