What is jump Discontinuity?

1 Answer
Amory W.
Aug 19, 2014

#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.

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