Limits for Complex Functions
Limits with and .
Use of mapping diagrams to visualize the definition of limits is not uncommon for real or complex analysis.
The strength of these visualizations is the power it gives to understanding how, where, and why the and are chosen.
First is chosen - arbitrarily - to identify an open region in the target containing the proposed limit number, .
Then a is chosen to identify an appropriate open region in the domain, containing the given point of interest, .
Finally it must be demonstrated that for any with in the domain , the value satisfies.
The following GeoGebra examples allow you to investigate the limit definition both when it fails and when it succeeds.