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(Section 2.8: Continuity)
2.8.7
PART D: CONTINUITY ON AN OPEN INTERVAL
Definition of Continuity on an Open Interval
Assume that
a
and
b
are real constants such that
a
<
b
.
A function
f
is continuous on the open interval
a
,
b
()
±
f
is continuous at every number (point) in
a
,
b
.
This extends to unbounded open intervals of the form
a
,
±
,
±²
,
b
, or
,
²
.
In Example 6, all three functions are continuous on the interval
0,
±
.
The first two functions are also continuous on the interval
,0
.
We say that the continuity set
(in interval form) of the first two functions is
³
0,
²
, because that is the set of all real numbers at which those
functions are continuous. (See Footnotes 3 and 5.)
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 Fall '10
 sturst
 Continuity

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