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2
1
1
lim
1
x
x
x
→
−
−
THE LIMIT OF A FUNCTION
Example 1 (2.2)
Guess the value of
.
±
Is f(x) defined when
x
= 1?
±
Does this affect the limit of f(x) as x approaches
1?
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View Full Document The tables give values
of
f
(
x
) (correct to six
decimal places) for
values of
x
that
approach 1 (but are not
equal to 1).
±
What is
?
THE LIMIT OF A FUNCTION
Example 1
Example 1 is illustrated by the graph
of
f
in the figure.
THE LIMIT OF A FUNCTION
Example 1
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View Full Document Now, let’s change
f
slightly by
giving it the value 2 when
x
= 1 and calling
the resulting function
g
:
()
2
1
1
1
21
x
if x
gx
x
if
x
−
⎧
≠
⎪
=
−
⎨
⎪
=
⎩
THE LIMIT OF A FUNCTION
Example 1
This new function
g
still has the
same limit as
x
approaches 1.
THE LIMIT OF A FUNCTION
Example 1
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View Full Document Investigate
.
±
Is
f
(
x
) defined at 0?
±
Does it affect the limit of f(x) as x approaches
0?
0
limsin
x
x
π
→
THE LIMIT OF A FUNCTION
Example 4 (2.2)
Evaluating the function for some small
values of
x
, we get:
Similarly,
f
(0.001)
=
f
(0.0001) = 0.
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.
 Fall '08
 Noohi
 Calculus

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