## anonymous 5 years ago What is the limit as x goes to infinity of ((ln x)^p)/x?

1. anonymous

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?

2. anonymous

i think it s correct way and u take p times

3. anonymous

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.

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

is ok?

8. anonymous

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