Math Help - Limit Problem

1. Limit Problem

Hi, I have been having troubles with one limit problem in particular:

Limx->inf cot(pi/4x)/x

Applying L'Hopital's rule only seems to make things worse. If anybody could help and show me what I should do to solve this limit, I would very much appreciate it. Thanks guys!

2. Re: Limit Problem

Hey Maburo.

What did you get when you applied L'Hopitals rule? The x in the denominator should disappear leaving the derivative of the cot term.

3. Re: Limit Problem

Applying L'Hopital's rule gives Limx->infinity (pi*csc^2(pi/4x))/(4x^2). This is again in an indeterminate form, and continuing to apply L'Hopital's rule will only further increase the degree of the 'x' variable in the denominator, plus make the limit quite ugly. I tried using a limit calculator which shows steps, but it tells me that the steps cannot be displayed.

5. Re: Limit Problem

Thank you very much! That seems like a useful method for solving limits, and I am sure that will come in handy. I really appreciate it!