1. ## Finding limits...

$
\lim_{x \to 0} {{tan3x}} / {{sin8x}}
$

Can I take the 3/8 out and just multiply it at the end? In any case, I can't find the limit!

I know $
\lim{x /to 0} {{sinx}} / {{x}} = 1
$
but I can't figure out how to get it to work out in this problem...

Also, where can I learn the proper math notation (ie \lim_{x \to 0} {{tan3x}} )?

2. Originally Posted by tom ato
$
\lim_{x \to 0} {{tan3x}} / {{sin8x}}
$

Can I take the 3/8 out and just multiply it at the end? In any case, I can't find the limit!

I know $
\lim{x /to 0} {{sinx}} / {{x}} = 1
$
but I can't figure out how to get it to work out in this problem...

Also, where can I learn the proper math notation (ie \lim_{x \to 0} {{tan3x}} )?

$\lim_{x\to0}\frac{\tan(3x)}{\sin(8x)}=\lim_{x\to0} \frac{\displaystyle\frac{\sin(3x)}{\cos(3x)}}{\sin (8x)}=\lim_{x\to0}\frac{\sin(3x)}{\sin(8x)}\cdot\l im_{x\to0}\frac{1}{\cos(3x)}=\lim_{x\to0}\frac{\si n(3x)}{\sin(8x)}$

Now, try to incorporate $\lim_{x\to0}\frac{\sin x}{x}$ into this limit.

Can you take it from here??