Calculus 2.2

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2.2 Limits Involving Infinity
North Dakota Sunset
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As the denominator gets larger, the value of the
fraction gets smaller.
There is a horizontal asymptote if
or
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Example 1
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Example 2
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Example 3
Find
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Infinite Limits
As the denominator approaches zero, the value of
the fraction gets very large.
vertical asymptote at x0.
If the denominator is positive then the fraction
is positive.
If the denominator is negative then the fraction
is negative.
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Example 4
The denominator is positive in both cases, so the
limit is the same.
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End Behavior Models
End behavior models model the behavior of a
function as x approaches infinity or negative
infinity.
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Example 7
(The x term dominates.)
Test of model
Our model is correct.
Test of model
Our model is correct.
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Example 7
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Example 7
Right-end behavior models give us
dominant terms in numerator and denominator
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Often you can just think through limits.
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