WEBVTT

1
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We want the limit of x squared minus nine, over x minus three, as x approaches three.

2
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Substituting three gives zero over zero, which is indeterminate. It does not mean the limit fails to exist.

3
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The numerator is a difference of squares: x minus three, times x plus three.

4
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For every x other than three, the common factor cancels, leaving x plus three.

5
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A limit only cares about values near three, so the limit is three plus three, which is six.

6
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The graph is the line y equals x plus three, with a hole at three comma six.

7
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The function is undefined at three, but its values approach six from both sides.

8
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To recap: zero over zero is a signal to simplify. Factor, cancel, then substitute again.