lim as x approaches pi (π)
Sin(π-x)
(π-x)

Two ways to solve this:

1. If you substitute u = \pi - x , you get:


\lim _ {x \to \pi} \frac {sin(\pi - x)} {\pi - x} = \lim _{ u \to 0} \frac {sin(u)} u


This second form may look familiar to you.

2. Have you studied l'Hospita'ls rule yet? It's quite handy: the limit as x appraches c for a function composed of a numerator and a denominator is equal to the limit as x approaches c of the derivative of the numerator over the derivative of the denominator:


\lim _{x \to c} \ \frac { f(x)} {g(x)} = \lim _{x \to c} \ \frac {f'(x)} {g'(x)}