# How to check if this function is continuous

1. Jun 2, 2014

### MissP.25_5

Hello.
The question is in the attached, together with my attempt. As you can see, I found the limit, but I don't know what each value means. If I have calculated the limits correctly, how do I know know if f(z) is continuous at 0 or not?

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2. Jun 2, 2014

### benorin

You have two different answers for the limit along different paths so the limit does not exist, therefore f(z) is not continuous at z=0.

3. Jun 2, 2014

### MissP.25_5

So, if no.1 and no.2 both had +/-1 as limits, then the function would be continuous at 0?

4. Jun 2, 2014

### benorin

No, if one is positive 1 and the other is negative 1, they are still different and thus the limit d.n.e. So it's not continuous there.

5. Jun 2, 2014

### MissP.25_5

Got it, thanks! By the way, could you look at my thread entitled contour integral please?