Determine the following limit$.$

$\backslash$lim$\_\{$x $\backslash$to $\backslash$infty$\}\backslash$frac$\{42$x$^3+3$x$^2-4$x$\}\{30$x$^3+$ x$^2+3$x $+3\}$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\backslash$displaystyle $\backslash$lim$\_\{$x $\backslash$to $\backslash$infty$\}\backslash$frac$\{42$x$^3+3$x$^2-4$x$\}\{30$x$^3+$ x$^2+3$x $+3\}=\backslash$boxed$\{\backslash$phantom$\{$answer$\}\}($Simplify your answer.$)$

B$.$The limit as x approaches $\backslash$infty does not exist and is neither $\backslash$infty nor $-\backslash$infty$.$