Yes, that's correct.

But you do not have , you have(b)

I can't prove that the limit doesn't exits because it turns out it exists:

(since limit as x ->0 sinx/x=1)

I'm confused can anyone help?

Look at the two one sided limits, as x goes to 0 from above and as x goes to 0 from below, remembering that for x< 0, sin(|x|)= sin(-x)= - sin(x).