The difference between the proof of continuity and uniform continuity of function

The difference between the proof of continuity and uniform continuity of function

① Continuity is defined from a point. X0 is a point in the domain of definition. For any ε > 0, there exists δ > 0, so that | x-x0 | 0 can be related to both x0 and ε. For different x0, even if the given ε is the same number, the found δ is often different

Proof method of function continuity!

There is no special formula or theorem, but I can sum up a few methods to show you
If a multivariate function is continuous, then the general method is as follows: H (x)

Definition of derivability and continuity of function? What is the relationship between them?

If f (x) is continuous at x0 and [f (x + a) - f (x)] / A has a limit, then f (x) is differentiable at x0