# Thread: Problem Finding A Limit

1. ## Problem Finding A Limit

I am just starting Calculus II, and I have thrown everything I know at this thing, to no avail

$\displaystyle \lim_{x \to \infty} (x sin\frac{\Pi}{x})$

Also, is there a guide for [,math] [/.math]? I swear the amount of time it took me to figure it out... you're damn lucky I am going into Computer Science! =P

Any assistance is greatly appreciated.

2. Hello, wm_hunter!

It looks suspiciously like: .$\displaystyle \lim_{\theta\to0}\frac{\sin\theta}{\theta} \:=\:1$

$\displaystyle \lim_{x \to \infty} \left(x\cdot\sin\tfrac{\pi}{x}\right)$

We have: .$\displaystyle x\cdot\sin\tfrac{\pi}{x} \:=\:\frac{\sin\frac{\pi}{x}}{\frac{1}{x}} \:=\:\frac{\pi}{\pi}\cdot\frac{\sin\frac{\pi}{x}}{ \frac{1}{x}} \:=\:\pi\cdot\frac{\sin\frac{\pi}{x}}{\frac{\pi}{x }}$

Now, as $\displaystyle x\to\infty,\;\frac{\pi}{x} \to 0$

So we have: .$\displaystyle \lim_{\frac{\pi}{x}\to0}\left(\pi\cdot\frac{\sin\f rac{\pi}{x}}{\frac{\pi}{x}}\right) \:=\:\pi\cdot1 \:=\:\pi$

3. Thank you. I can see the solution and I understand, it does seem a little complicated, but if it wasn't I wouldn't be on here asking for help