Question

What is jump Discontinuity?

Answer 1

`lim_(x->a^-)f(x), lim_(x->a^+)f(x)` are finite and `lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)`. So it occurs when the left and right limit at `a` do not match, then we say `f(x)` has a jump discontinuity at `a`.

This should not be confused with a point discontinuity where:

`lim_(x->a^-)f(x)=lim_(x->a^+)f(x)`

which means

`lim_(x->a)f(x)` exists

and:

`lim_(x->a)f(x)!=f(a)`

It could be the case that `f(a)` is finite or simply DNE.