Question

Can You tell me how to find the limit of the below expression?

Answer 1

\[y = \lim_{x \rightarrow \infty} \ (1/x)^{\tan x}\]

Answer 2

I think we should use Hopital, but I don't know how to deal with tan when x tends to infinity!

Answer 3

I think you have to take natural log on both sides..\[\large \ln(y) = tanx \ln(\frac{1}{x})\]

Answer 4

And then re-arrange the terms so you get 0/0 or infinity/infinity so you can use L'Hospitals Rule.

Answer 5

Tyler,
Yes, I did it. But how should I deal with tan x when x -> infinity?

Answer 6

Either way you should find it doesn't have a limit at infinity.

Answer 7

That ln() function mentioned above blows up to infinity at periodic intervals, so it can't have a limit.

Answer 8

^ ahh thats true.. So the limit DNE

Answer 9

I should be more specific.... it cannot have a limit at infinity or any of the points
\[x = \frac{\pi}{2} + n\pi\]

Answer 10

I see!
Thanks.