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| ALGEBRA
- solved problems |
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The
limit of a function
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| Limits of
rational
functions |
| A
rational function is the ratio of two polynomial functions |
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| where
n and m
define the degree of the numerator and the denominator
respectively. |
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| Evaluating
the limit of a rational function at infinity |
| To
evaluate the limit of a rational function at infinity
we divide both the numerator and the denominator of
the function by the highest
power of x
of
the denominator. |
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Evaluate
the limit |
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| Solution:
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Evaluate
the limit |
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| Solution:
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Evaluate
the limit |
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| Solution:
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Evaluating
the limit of a rational function at a point
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a)
The limit of a rational function that is defined at the given point
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Evaluate
the limit |
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| Solution:
We first factor
the numerator and denominator |
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| Since
q(1/2) is
not
0
then |
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| x
= 0
and x
= 1
are vertical asymptotes, and y
= 1
is the |
| horizontal
asymptote, as is shown in the right figure. |
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b)
The limit of a rational function that is not defined at the
given point
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Evaluate
the limit |
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| Solution:
To avoid the indeterminate form 0/0,
the expression takes as x
®
1,
we factor and cancel common
factors |
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The rational function has the hole in the graph at x
= 1, |
| the vertical
asymptote
x
= -1
and
the horizontal |
| asymptote
y
= 2
since |
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| as is shown in the right figure. |
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| Solved
problems contents - A |
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| Copyright
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