Question

How do you find jump discontinuity?

Answer 1

There are 2 ways, you can look at a graph or you can use the definition.

Using the definition, show:

`lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)` and both are finitie

It is important that they are finite. If one is not finite or does not exist, then it would be infinite discontinuity.

Using a graph, it's the same thing; both the red and blue functions have jump discontinuity:

Let's say the red function, `f`, is discontinuous at `a` and the blue, `g`, at `b`. Notice:

`lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)` and `f(a)` `DNE`
`lim_(x->b^-)g(x)!=lim_(x->b^+)g(x)` and #lim_(x->b^-)g(x)= g(b)#