Question

limit theta approaches 0 tan theta/theta

Answer 1

you know
\[\lim_{x\to 0}\frac{\sin(x)}{x}\]?

Answer 2

yeah but here "theta" is placed in the place of "x" while "tan" is placed in the place of "sin".

Answer 3

For the record,\[\lim_{x\to0}f(x)=\lim_{\theta\to0}f(\theta)\]
The variables \(x\) and \(\theta\) are interchangeable; that's what variables represent.

As for the limit,
\[\lim_{\theta\to0}\frac{\tan\theta}{\theta}=\lim_{\theta\to0}\frac{\sin\theta}{\theta\cos\theta}=\left(\lim_{\theta\to0}\frac{\sin\theta}{\theta}\right)\left(\lim_{\theta\to0}\frac{1}{\cos\theta}\right)\]