For , show that the following limit exists:

How to define when in such a way to make f continuous?

Thanks.

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- Jan 23rd 2009, 02:31 PMtttcomraderContinuous with limit
For , show that the following limit exists:

How to define when in such a way to make f continuous?

Thanks. - Jan 23rd 2009, 02:43 PMvincisonfire
If then you then the range is a unit disk down at -1 on the z-axis. (supposing you work in "kind of" )

- Jan 24th 2009, 04:25 PMThePerfectHacker
Since it means or .

If it means because .

Thus, in that case .

If then because .

The function cannot be extended to a continous function on . This is because is not continous on . It has one value inside the disk and it has another values outside the disk. Thus, it cannot be continous.