How do you find jump discontinuity?

Question

9723 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-09-05T01:03:46

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:
enter image source here

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 $lim_(x->b^-)g(x)= g(b)$