# Thread: Evaluate the limit

1. ## Evaluate the limit

Evaluate the limit of
$\lim_{x \to \pi} \frac {sin^2{x}} {1+cos{3x}}$

I assume I use L'Hopital's rule here?
This gives me:
$\frac {sin{2x}} {-3sin{3x}}$
which comes to 0/0.
wanting some reassurance here that I'm on the right track!

2. Originally Posted by Dr Zoidburg
Evaluate the limit of
$\lim_{x \to \pi} \frac {sin^2{x}} {1+cos{3x}}$

I assume I use L'Hopital's rule here? <<<<<<< OK
This gives me:
$\frac {sin{2x}} {-3sin{3x}}$
which comes to 0/0.
wanting some reassurance here that I'm on the right track!
I would use:

$\lim_{x \to \pi} \frac {sin^2{x}} {1+cos{3x}} = \lim_{x\to \pi}\dfrac{2 \sin(x) \cdot \cos(x)}{-3\sin(3x)}$

As long as the quotient becomes $\frac00$ you can apply l'Hopitals's rule.

In the end you should get $\frac29$

3. In other words, apply L'Hopital's rule again!

4. cool. Got it now.
Thanks all for your help. I'm doing this paper by correspondence so this is the only place (other than the textbooks) I can turn for advice/help when I get stuck or just when I want confirmation I'm on the right track.