# Thread: limit question

1. ## limit question

Why is this right

$\frac{1}{2}\frac{\lim}{u\rightarrow0}\frac{\sin[u]}{u}=\frac{1}{2}$

I can make it work with L'Hop's but is it legal to use when u approaches 0 and not infinity

2. Yep. You can use L'Hop for this case too. There are also other ways of proving this identity.

3. Thanks Rangr. Can L'Hops be used for u=any N

4. L'Hops can be used if you have 0/0 or 0/infinity or infinity/infinity or infinity/0. i.e. functions not evaluable at their limits, so we evaluate their slopes when they tend towards these limits.