Calculating the value of the limit $$\lim_{(x,y)\to(1,2)}(\sin(y)-\sin(x))$$
My try:
I got as $$\sin(2)-\sin(1)$$
But I cannot calculate the exact value of the given limit. Can anyone please explain this.

Yes your result is correct, indeed since the function is continuous at the point we have
$$\lim_{(x,y)\to(1,2)}(f(x,y))=f(1,2)$$
that is 
$$\lim_{(x,y)\to(1,2)}(\sin(y)-\sin(x))=\sin 2 -\sin 1$$
where $2$ and $1$ are expressed in radians, a numerical evaluation leads to $\approx 0.068$.
