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Easy: Differences of squares
If substituting gives 0/0, the top and bottom share a factor (x − a). Factor both, cancel it, and substitute into what is left. The function has a hole at x = a, but the limit still exists. With a square root, multiply the top and bottom by the conjugate first.
Evaluate each limit.
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Neither. 0/0 is an indeterminate form: it tells you to simplify. After factoring and cancelling, substitution usually gives the limit.
A limit only looks at x near a, never at a itself. For every x ≠ a the cancelled expression has the same value, so the limits are equal.
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