Question

I am learning calculus, and have been stuck on this question. I cannot use Ls Hospital Rule to solve it and i’m stuck after one step

Answer 1

Using the trigonometric identities given, we get:

`\begin{gathered} \lim _(\theta\rightarrow0)\text{ }(\cos(\theta+A)-\cos(\theta-B))/(\theta)=\lim _(\theta\rightarrow0)(\cos \theta\cos A-\sin \theta\sin A-(\cos \theta\cos B-\sin \theta\sin B))/(\theta) \\ =\lim _(\theta\rightarrow0)(\cos \theta(\cos A-\cos B)+\sin \theta(\sin B-\sin A))/(\theta) \\ =\lim _(\theta\rightarrow0)(\cos\theta)/(\theta)(\cos A-\cos B)+\lim _(\theta\rightarrow0)(\sin \theta)/(\theta)(\sin B-\sin A) \end{gathered}`

Recall that:

`\lim _(\theta\rightarrow0)(\cos\theta)/(\theta)\text{ does not exist.}`

And the limit of the product is the product of the limits.

Therefore the limit of interest does not exist.