Question

What is the difference between a jump and a removable discontinuity?

Answer 1

Their limit definitions and appearance on a graph.

Explanation:

This is a jump discontinuity.
In a jump discontinuity, `lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)`. That means, the function on both sides of a value approaches different values, that is, the function appears to "jump" from one place to another.

This is a removable discontinuity (sometimes called a hole).

Here, the function appears to come to a point, but the actual function value is elsewhere or does not exist.This can be written as `lim_(x->a^-)f(x)=lim_(x->a^+)f(x)!=f(a)`