(x/6) sqrt(x-1) / sqrt(x^2 - 1)
divide top and bottom by x:
(x/6) sqrt(x-1) / sqrt(x^2 - 1) = (1/6) sqrt(x-1) / sqrt(1 - 1/x^2)
Now as x -> inft the denominator goes to 1, and the numerator goes to infty.
Therefore the limit of this term is +infty.
The other terms are all positive for large x, so it does not matter how they
behave for large x we still have:
lim(x->infty) f(x) = infty