lim x->a [f(x) - f(a)]/(x - a)

Continuity: Continuity refers to when a function has no breaks or jumps and can be drawn without lifting your pen from paper. It ensures that limits exist at every point within an interval.

Differentiability: Differentiability describes a function that has a derivative at every point within an interval. It means the function is smooth and has a well-defined slope at each point.

Removable Discontinuity: A removable discontinuity occurs when there's a hole in the graph of a function, but it can be filled by redefining the value of the function at that specific point. It's like having a gap in your dartboard, but you can place a sticker to cover it up and make it continuous again.