Find the trigonometric limit: lim (as x approaches infinity) (x-tan 2x)/sin 2x

Printable View

- Dec 30th 2005, 07:53 PMbobby77please help -urgent
Find the trigonometric limit: lim (as x approaches infinity) (x-tan 2x)/sin 2x

- Dec 30th 2005, 11:10 PMrgep
We have $\displaystyle \frac{x - \tan 2x}{\sin 2x} = \frac{x}{\sin 2x} - \frac{1}{\cos 2x}$. Now consider the subsequences $\displaystyle x = 2\pi n + \frac\pi2$ and $\displaystyle x = 2\pi n + \pi + \frac\pi2 $ to see that there is no limit.

- Dec 30th 2005, 11:29 PMCaptainBlackQuote:

Originally Posted by**rgep**

and $\displaystyle x=\pi/4+n.\pi$ for $\displaystyle n=1,2,..$ to show that it does not go to $\displaystyle +\infty$?

RonL - Dec 31st 2005, 10:01 PMticbolQuote:

Originally Posted by**bobby77**

If it is as x approaches infinity, then what is tan(infinity)? Or, sin(infinity)?

If x approaches zero, limit is (-1/2).