Limit of piecewise function using epsilon delta

[FactChecker]

By minimum, do you mean $\delta=\text{min}~(1, \frac{\epsilon}{4})$?

Sorry, my mistake.
I didn't realize that this example is different from the one in post #1. In this example, one function equation works for both sides, so you only get one value for $\delta$ that works for both sides. Taking a minimum is necessary if you get two different answers for $\delta$ for two sides. In that case you should take the minimum of them. Then the minimum would work for both sides.

 

[songoku]

I am very sorry for late reply

Thank you very much for all the help and explanation pasmith, PeroK, FactChecker, BvU, Gavran, anuttarasammyak