I have the following two problems I am working on:
For this one I am using the limit comparison test, I did
f(x)= 1/(x^3-1)^1/2 / g(x) = 1/x
which ended up at x/(x^3-1)^1/2 which I can determine as x->infty is going to be greater than 0 but less than infinity (thus both either converge or diverge). I then integrated my g(x) which I chose as 1/x and got as a limit infty, thus the functions diverge. Is this correct?
The second one is:
For this one I took a similiar approach, except g(x) = x^2/sqroot(x^8) and determined f(x)/g(x) = 1, thus greater than zero but less than infty. So I integrated my g(x) down to -1/x, and as x->infty the limit is zero. No positive finite limit, thus it diverges.
Hope I'm doing these right. Any help would be great thanks in advance.