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