MATH 1225 Lecture 10: Sec 2.2 (1) (1)
28 May 2018
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Department
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Sec. 2.2 The Limit of a Function
EX: Let
3
9
2
x
x
xf
1. Determine the domain of
xf
2. Given the table below, what is the value that
xf
approaches as
3x
? That is, what is
xf
x3
lim
?
x
xf
x
xf
2.9
5.9
3.1
6.1
2.99
5.99
3.01
6.01
2.999
5.999
3.001
6.001
2.9999
5.9999
3.0001
6.0001
Note: Oftentimes, the table of values can be misleading in finding limits. See example 4 and 5 from text book (page
86-87) for examples.
Notice:
,3
3
33
3
9
2
x
x
xx
x
x
xf
for
3x
• Definition of a limit:
Suppose
xf
is defined when
x
is near the number
a
. Then we write
Lxf
ax
lim
and read “the limit of
xf
, as
x
approaches
a
, equals
L
”
If we can make the values of
xf
arbitrarily close to
L
(as close to
L
as we like) by restricting
x
to be
sufficiently close to
a
(on either side of
a
) but not equal to
a
.
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Document Summary
Xf: given the table below, what is the value that x. Note: oftentimes, the table of values can be misleading in finding limits. See example 4 and 5 from text book (page. Xf is defined when x is near the number a . L xf lim x a and read the limit of. , as x approaches a , equals l . If we can make the values of arbitrarily close to l (as close to l as we like) by restricting x to be sufficiently close to a (on either side of a ) but not equal to a . L xf: we write lim x a and say the left-hand limit of. Xf as x approaches a [or the limit of. Xf as x approaches a from the left] is equal to l if we can make the values of.
