Find the limit or show that it does not exist.
lim (sqrt(t)+t^2)/2t-t^2) as t approaches infinite

Question

Find the limit or show that it does not exist.
lim (sqrt(t)+t^2)/2t-t^2) as t approaches infinite

jkristia · Answer

I would say the limit is -1 since you basically have (x / (-x)) at infinity

anonymous · Answer

That is the correct answer but how do you solve it out to that, is what i'm struggling with.

jkristia · Answer

I can't figure out how to simplify it either so the term can be cancelled and you are left with x / -x. But since this is a rational function, and the degree is the same in the numerator and denominator, then you know you have a horizontal asymptote at a/b, in this case 1 / -1 when x -> infinity.

anonymous · Answer

Hm make's sense if i think about horizontal asymptote. Thank you

anonymous · Answer

take t^2 out and u get$$((1\div t^{1.5})+1)\div((2\div t)-1)$$
as t tends to infinity, the equation reduces to 1/-1.
so the answer is -1