Use continuity to evaluate the limit:

[girlnamedbrigid]

lim as x approaches pi, sin(x + sin(x))

Any help working through this would be nice. I'm not sure where to even begin. Thank you.

 

[galactus]

The function is continuous at a point if the following conditions hold:

1. $\displaystyle sin(x+sin(\pi))$ is defined

2. $\displaystyle \lim_{x \to \pi}sin(x+sin(x))$ exists.

3. $\displaystyle \lim_{x \to {\pi}}sin(x+sin(x))=sin(\pi+sin({\pi}))$

That is all there is to it.

 

[fasteddie65]

Just in case, sin(x + sin ?) = sin (x + 0) = sin x