- If limx→a+f(x) and
limx→a−f(x) both exist, but are different,
then we have a jump discontinuity. (See the
example below, with a=−1.)
-
If either limx→a+f(x)=±∞ or limx→a−f(x)=±∞, then we have an infinite discontinuity,
also called an asymptotic discontinuity. (See
the example below, with a=−1.)
-
If limx→a+f(x) and
limx→a−f(x) exist and are
equal (and finite), but
f(a) happens to be different (or doesn't exist), then
we have a removable discontinuity, since by
changing the value of f(x) at a single point we can
make f(x) continuous. (See the example below, with
a=1.)
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