Question

use continuity to evaluate the limit as x approaches pi of sin(x+sinx)

Answer 1

\[\lim_{x\to\pi}\sin(x+\sin x)=\sin\left(\lim_{x\to\pi}(x+\sin x)\right)\]
This is what it means to use the continuity of a function in a limit. Sine is continuous as its argument approaches \(\pi\), so you can evaluate the limit this way.