1. Limits to define continuity
You might have an intuitive idea of continuity, but how do you define it? Using limits!
2. Limit and function defined at point of discontinuity
Based on out definition of continuity, we can see the relationship between points of discontinuity and two-sided limits.
3. Fancy algebra to find a limit and make a function continuous
If a function is discontinuous at a point, but the two sided limit around that point exists, you can make the function continuous by tweaking its definition.
4. Defining a function at a point to make it continuous
Sometimes when a function is discontinuous at a point, you can make it continuous by giving it a value at that point.