# How do you find #\lim _ { \theta \rightarrow 0} \frac { \cos ( 7\theta ) - 1} { \sin ( 4\theta ) }#?

##### 1 Answer

#### Explanation:

We first just try plugging in

This results in the indeterminate form

There is however a trick you can use to evaluate limits of this indeterminate form. It's called L'Hôpital's Rule. It basically says that if both the top and the bottom tend to

If

Then

Applying this to our case, we get:

The derivatives can be computed using the chain rule:

Now we put back into the limit and evaluate at