Question

What did sin theta/theta whisper worksheet answer key worksheet?

Answer 1

To evaluate

`\lim_(\theta \to 0) (\sin\theta)/(\theta)`

First, we input 0, for theta in the function to obtain:

`(\sin0)/(0) = (0)/(0)`

This is an indeterminate form.

So, we apply L'Hopital's rule by differentiating the numerator and the denominator as follows:


`\lim_(\theta \to 0) (\sin\theta)/(\theta)=\lim_(\theta \to 0) ( (d)/(d\theta) (\sin\theta))/((d)/(d\theta)\theta) \\ \\ =\lim_(\theta \to 0) (\cos\theta)/(1)=\cos0=1`