Limit gives the approaching value of the function when you start going close to the point.
1. If you start reaching the point say 'a' from right side means values you are crossing to reach 'a' are just greater than 'a', then the curve also approach to some fixed number. That number is right hand limit of the function 'f(x)' when x approaches that point 'a'.
2. If you start reaching the point say 'a' from left side means values you are crossing to reach 'a' are just smaller than 'a', then the curve also approach to some fixed number. That number is left hand limit of the function 'f(x)' when x approaches that point 'a'.
3. If Right hand limit = Left hand limit and are finite numbers, then we say limit exist.
4. If there's is no break in the graph of the function around that fixed point, then right hand limit is always equal to left hand limit and gives us limit of the function.
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