How do you find jump discontinuity?

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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)#