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(Section 1.5: PiecewiseDefined Functions; Limits and Continuity in Calculus)
1.5.11
PART G: CONTINUITY IN CALCULUS
f
is continuous
at
a
, or
x
=
a
±
1)
fa
()
is defined,
2)
lim
x
±
a
fx
exists, and
3)
lim
x
±
a
=
.
f
is discontinuous
at
a
±
f
is not continuous at
a
.
(Some sources require that
f
be defined “around”
a
.)
Comments
1)
ensures that there is literally a point at
a
.
2)
constrains the behavior of
f
immediately around
a
.
3)
then ensures safe passage through the point
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This document was uploaded on 12/29/2011.
 Spring '09
 Continuity, Limits

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