# Question #99ee1

##### 1 Answer

A function

#lim_{x\to x_0} f(x)=f(x_0)#

Which means that, if you consider the limit of

Visually, this means that you can bring the limit "inside" the function, in this sense:

#lim_{x\to x_0} f(x)=f(lim_{x\to x_0}x)#

This given, your solution is thus

#\lim_{x\to\pi} \sin(x+\sin(x))=#

#\sin(\lim_{x\to\pi} (x+\sin(x)))#

Now, of course

#\sin(\lim_{x\to\pi} (x+\sin(x)))=#

#\sin(\pi+\sin(\lim_{x\to\pi} x)=#

#\sin(\pi+\sin(\pi))#

And since

#\sin(\pi+\sin(\pi))=#

#\sin(\pi+0)=\sin(\pi)=0#

Here're the graph of the function, showing both that the function is continuous (even if it's not a proof of course), and that

graph{x+sin(x) [-10, 10, -5, 5]}