Discontinuity
Discontinuity
For a value , let = (the limit from the left) and = (the limit from the right).
f(s)
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lim
xs

f(x)
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+
lim
xs
+
f(x)
If = = , the function is continuous at .
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L
+
f(s)
x=s
If = ≠ , the function has a removable discontinuity at .
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L
+
f(s)
x=s
If ≠ , and both values are finite, the function has a jump discontinuity at .
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L
+
x=s
If ≠ , and one or both values is infinite, the function has an infinite discontinuity at . This is also called an essential discontinuity.
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L
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x=s