MATH 1225 Lecture 6: Sec 2.4 (1) (1)
28 May 2018
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Sec. 2.4 The Precise Definition of a Limit
• Precise definition of a limit: Let
f
be a function defined on some open interval that contains the number
a
,
except possibly at
a
itself. Then we say that the limit of
xf
as
x
approaches
a
is
L
, and we write
Lxf
ax
lim
if for every number
0
there is a number
0
such that if
ax0
then
Lxf
Note:
= read “epsilon”, our margin of error
= read “delta”
• What do
ax0
and
Lxf
mean?
EX: Let
12 xxf
1. Find
xf
x2
lim
2. What is the largest interval containing
2x
such that the graph of
xfy
is within 1 unit of
xf
x2
lim
3. What happens to the x-interval if we want the graph of
xfy
to be closer to the value of the limit?
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Document Summary
2. 4 the precise definition of a limit: precise definition of a limit: let f be a function defined on some open interval that contains the number a , except possibly at a itself. Then we say that the limit of as x approaches a is l , and we write. L lim xf x a xf. Note: = read epsilon , our margin of error. Xf: what is the largest interval containing. 2 x such that the graph of y . 2: what happens to the x-interval if we want the graph of y . 1 , what is needed to be to satisfy the condition (use the graph to find ): find the largest value of. If it does not exist: find the largest. If it does not exist, explain: find the largest. If it does not exist, explain why: find the largest. If it does not exist, explain why: definition of left-hand limit: ax a then xf.
