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2.2
Limits Involving Infinity
Greg Kelly, Hanford High School, Richland, Washington
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1
f x
x
=
1
lim
0
x
x
x
=
As the denominator gets larger, the value of the fraction
gets smaller.
There is a horizontal asymptote if:
( 29
lim
x
f x
b
x
=
or
( 29
lim
x
f x
b
g

=
→
2
lim
1
x
x
x
x
+
Example 1:
2
lim
x
x
x
x
=
This number becomes insignificant as
.
x x
&
lim
x
x
x
x
=
1
=
∴
There is a horizontal asymptote at 1.
→
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View Full Document ( 29
sin
x
f x
x
=
Example 2:
→
sin
lim
x
x
x
→∞
Find:
When we graph this
function, the limit appears
to be zero.
1
sin
1
x
 ≤
≤
so for
:
0
x
1
sin
1
x
x
x
x

1
sin
1
lim
lim
lim
x
x
x
x
x
x
x

sin
0
lim
0
x
x
x
→∞
≤
≤
∴
by the sandwich
theorem:
sin
lim
0
x
x
x
→∞
=
Example 3:
5
sin
lim
x
x
x
x
→∞
+
Find:
5
sin
lim
x
x
x
x
x
→∞
+
sin
lim5
lim
x
x
x
x
→∞
→∞
+
5 0
+
5
→
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View Full Document Infinite Limits:
( 29
1
f x
x
=
0
1
lim
x
x
+
→
= ∞
As the denominator approaches
zero, the value of the fraction gets
very large.
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This note was uploaded on 03/10/2008 for the course MATH 131 taught by Professor Riggs during the Fall '05 term at Cal Poly Pomona.
 Fall '05
 Riggs
 Differential Calculus, Limits

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