Limits At Infinity 12.14.07
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8 6 4 2 -2 -4 -6 -10 -5 5 10 Limits at Infinity (Horizontal Asymptotes) .. x As . 0 ... y . 0 1 lim So, 2 x x 2 1 ) ( x x f
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Transcript of Limits At Infinity 12.14.07
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6
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2
-2
-4
-6
-10 -5 5 10
Limits at Infinity(Horizontal Asymptotes)
... xAs
.0... y
.01
lim So,2x
x
2
1)(x
xf
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3.5
3
2.5
2
1.5
1
0.5
-0.5
-1
-1.5
-2
-2.5
-4 -3 -2 -1 1 2 3 4 5
0lim rx x
c
3
1)(x
xf x
xf1
)(
The Golden Rule…
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-1
-2 2 4 6 8 10 12
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-1
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-6 -4 -2 2 4 6
xxf
1)(
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xx
13lim
xxx
1lim3lim
10
8
6
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2
-10 -5 5 10
3
03
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42
1lim
x
xx
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103
34lim
x
xx
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2
72lim
2
x
xx
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1
1lim
2
x
xx
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042
33lim
3
2
x
xxx
2
3
42
33lim
2
2
x
xxx
exist!not ...does 42
33lim
3
4
x
xxx
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Homework
p. 203 #9-18
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