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Suppose ƒ(
x
) is a realvalued function and
c
is a real number. The expression:
means that ƒ(
x
) can be made to be as close to
L
as desired by making
x
sufficiently close
to
c
. In that case, we say that "the limit of ƒ of
x
, as
x
approaches
c
, is
L
". Note that this
statement can be true even if
. Indeed, the function ƒ(
x
) need not even be defined
at
c
. Two examples help illustrate this.
Consider
as
x
approaches 2. In this case,
f
(
x
) is defined at 2 and equals
its limit of 0.4:
f
(1.9)
f
(1.99)
f
(1.999)
f
(2)
f
(2.001)
f
(2.01)
f
(2.1)
0.4121 0.4012 0.4001
0.4
0.3998
0.3988 0.3882
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This note was uploaded on 04/10/2008 for the course MATH 132 taught by Professor Julies during the Fall '08 term at Michigan State University.
 Fall '08
 Julies
 Limits

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