ok, so here is what we can do.
Lets look at the numerator then the denominator.
(11x^7+2x^5+x)
x^7 grows MUCH faster than x^5, or x, so as x approaches infinity, only the 11x^7 matters, so we will keep that.
lim as x -> infinity (11x^7+2x^5+x) = 11x^7
Similarly
lim as x -> infinity (7x^6+5x-8) = 7x^6
Now we have:
lim as x -> infinity [ (11x^7) / (7x^6) ]
lim as x -> infinity [ (11/7) * x ]
(11/7) * (infinity)
infinity
Done.
That is not the correct work to show, but it is to make sense to you.
I believe the answer is positive infinity
because the dominant power x^7 is in the NUMERATOR, top (oops confused the two)
and the sign of the coefficient 11 is positive
therefore making it positive infinity