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