Question

What is the limit as x goes to infinity of ((ln x)^p)/x?

Answer 1

I keep getting infinity over infinity no matter how many times I do L'Hopital's rule. What's the right way to do this?

Answer 2

i think it s correct way
and u take p times

Answer 3

That doesn't make sense. The problem is the derivative of (ln x)^p gives me 1/x as part of the answer. x goes into the denominator, and voila, the limit as x goes to infinity of x is infinity - thus the infinity over infinity. That's why I'm thinking I'm doing something wrong.

Answer 4

i think \[\lim_{x \rightarrow \infty}p!*1/x=0\]

Answer 5

Wouldn't that equal \[p!\lim_{x \rightarrow \infty} 1/x\] 0*p!=0. I don't get how that's relevant.

Answer 6

\[\lim_{x \rightarrow \infty}p*(p-1)*(p-2)*****2*1*1/x\]

Answer 7

is ok?

Answer 8

I'll see if I can turn that into a factorial somehow. Thanks.