Calculate lim x $->\backslash$infty ln$(3$x$)3$ x $.$ Solution Since ln$(3$x$)->\backslash$infty and $->\backslash$infty as x $->\backslash$infty $,$ l'Hospital's Rule applies. lim x $->\backslash$infty ln$(3$x$)3$ x $=$ lim x $->\backslash$infty $1$ x $13$ x$23=$ lim x$->\backslash$infty $1$ x $133$ x$2$ Notice that the limit on the right side is now indeterminate of type $00.$ But instead of applying l'Hospital's Rule a second time as we did in this example, we simplify the expression and see that a second application is unnecessary. lim x $->\backslash$infty ln$(3$x$)3$ x $=$ lim x$->\backslash$infty $1$ x $133$ x$2=$ lim x $->\backslash$infty $33$ x $=.$