Discontinuity Limits: Does f(b) Mean Discontinuous at x=b?

[Loppyfoot]

On the graph, the limit at a has a removable discontinuity at b. And below this, there is a darkened circle, which means that f(b) exists. Does this mean that f is discontinuous at x=b?

 

[VeeEight]

Use the fact that if a function is continuous at a, then any sequence x_n that converges to a will satisfy lim f(x_n) = f(a) as n tends to infinite. So if you can find two such paths that tend to different limits you will have shown that the function is discontinuous at that point