I am trying to learn some calculus and I see this in my textbook:
Why does
$$\lim_{\theta \to 0} \frac{-\sin^2\theta}{\theta\cdot ( \cos\theta + 1)}$$
$$ = $$
$$ -\lim_{\theta \to 0} \frac{\sin \theta}{\theta} \cdot \frac{\sin \theta}{\cos \theta + 1}$$
My question is about pulling out the negative sign from the numerator in the line 2 lines above this one to the line right above this one where the negative sign is outside of the limits
Is it because: $$-\sin^2\theta = $$ $$(-1)\cdot (\sin^2\theta)$$
and so when we take the limit of the numerator:
$$\begin{align} \lim_{\theta \to 0}(-1)(\sin^2\theta) &= \\ \lim_{\theta \to 0} (-1) \cdot \lim_{\theta \to 0} (\sin^2\theta) &= \\ -1 \cdot \lim_{\theta \to 0} (\sin^2\theta) \end{align}$$
Is that right? Is that how we pull out the negative sign?