Definition of Limits- If f(x) becomes arbitrarily close to a unique number L as x approaches c from either side, the limit of f(x) as x approaches c is L.
*Note- the limit doesn't care what is actually happening at c
Example-
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Example-
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Even though this graph has a hole at x=1, the graph still approaches 2 from both sides so the limit is still 2. The limit doesn't care what is actually happening at f(1).
Example-
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This limit does not exist because as x approaches 0, f(x) oscilalates between 1 and -1.
Properties of Limits-
