MA 109 Limits
With polynomial and rational functions, you can normally replace the variable by
the value you are approaching:
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However, you must avoid division by zero:
Here we cannot substitute -1. Instead, we reduce first:
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Limits at infinity are solved based on the fact that a constant over the variable
approaches zero as the variable goes to infinity. For example:
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Then, the limit at infinity of a rational function is handled by dividing the top and
bottom by the highest power of x found on the bottom.
Example 1:
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Example 2:
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Example 3: This uses the reciprocal of the last rational function.
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The limit at minus infinity works much the same way:
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