Question

need help...first time on site:

limit to inifinity of this
n^.5 plus n^(1/3) divided by
n + 2n^(2/3)

book pulled out n to the neg .5

not sure why. Am thinking there is a better way?
Don't you always divide by highest power?

Answer 1

IMO, if you divide everything by n^(2/3), you get:\[\frac{ n^{-\frac{1}{6}} +n^{-\frac{1}{3}}}{ n^{\frac{1}{3}}+2 }\]Now, if n goes to infinity, the powers of n in the numerator go to 0, the denominator goes to infinity, so the whole thing goes to 0.

So, I think you're right!

Answer 2

I believe you divide by the lowest power, which is 1/3. so it would be.