Calc1131W3T3 - Left-hand and right-hand limits

Friday, 23 March 2018

1:28 PM

Machine generated alternative text:
The in
This a a
L f(x) L. This
liau_
as ta a then f (r) gets to L Thi. of Mitten
lim = L.
22 1
.15, 1.021
x --004

Machine generated alternative text:
Recall thet either equals , il 0 or it equals —x, < O so problems Involving absolute values Often need to be split into two Whether What S inside the absolute s
pos•ttve, negative,
Consider the following example]
1-299
= 12.99,
12*-61
• Vind the left-hand brnlt lim
. Find right-hand limit lim
. Does lim
0
nat •

Machine generated alternative text:
Cornpt_Ae the wowing Jen-hand and right hand limits
0
r *0-+- 1511
2
0

Machine generated alternative text:
Sometimes functms are given In piece-wise such as
3
O
• lim_ f(r) =
0
lim
lim
• lim
lim
otherwise.
16
14
12
10
8
6
4
2
2
3
4

Machine generated alternative text:
Consider the function
For < 0, this function equals
For > 0. this furwt.on equals
lim g(r) =
So
lim g(x)
Hence lim
defined because the left and nght hand limits
equal

Created with Microsoft OneNote 2016.