I'm reading Boas' chapter on functions of a complex variable, and she's talking here about finding residues. However, I don't understand the evaluation of the limit(below). How is it that we can take $\cos(0)$ out of the limit while $\sin(z)$ and $z$ stay within the limit?
$ \lim_{z \to 0} \frac{z\cdot\cos(z)}{\sin(z)}=\cos (0)\cdot \lim_{z \to 0}\frac{z}{\sin(z)}=1\cdot 1=1 $