When you plug into a limit and get 0/0 or ∞/∞, you can differentiate the top and bottom separately and try again. That's L'Hôpital's rule.
L'Hôpital
lim f(x)/g(x) = lim f'(x)/g'(x)
when both → 0 or both → ∞
Try it
lim(x→0) sin(x)/x
Plugging 0 gives 0/0. Differentiate: cos(x)/1. At x=0: cos(0) = 1.