I'm struggling to evaluate this limit problem:

$$\lim\limits\_{(x,y) \to (\pi,0)} {\cos x + 1 + {y^2/2} \over (x - \pi)^2 + y^2}$$

I've tried this with paths $x=\pi$, $y=0$, $y=x-\pi$, ... and so far all of them have resulted in $1 \over 2$. However when I try to evaluate this in WolframAlpha, it says that the limit does not exist.

I haven't found any paths that result in a value other than $1/2$. How can I prove that this limit does not exist?