Well, I admit that I don't have a good grasp on limits of this nature, but I do know that
and that the limit of a sum is the sum of the limits.
I know I used good math here. The only part that I was unsure of was subtraccting infinity from infinity.
Could you please enlighten me with an explaination?
If this had been posted in the Calculus subforum you could now easily apply l'Hopital's rule.
However, without using l'Hopital's Rule, there's slightly (but not a lot) more work ..... multiply numerator and denominator by the conjugate surd (twice) and then cancel a common factor of t.
Either way, you get 0 as the answer.