# Thread: Trig Limit

1. ## Trig Limit

Hey

I know this question is rather simple but I just can't seem to get it...

$\displaystyle\lim_{x\rightarrow0}\frac{sin 5x}{sin 2x}-\frac{sin 3x}{4x}$

Thanks

2. You know the standard limit of sin(a)/a for a->0? It's 1. Rewrite:

$
\lim_{x\rightarrow0}\left( \frac{\sin 5x}{\sin 2x}-\frac{\sin 3x}{4x} \right) =
\lim_{x\rightarrow0}\left( \frac{5}{2} \frac{\sin 5x}{5x} \frac{2x}{\sin 2x}
-\frac{3}{4}\frac{\sin 3x}{3x} \right)
$

Now take the limit of both terms and in each term, of all factors.