Consider the terms separately. Look at the last one:

(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

RonL