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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