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A good place to start is to get an idea of what f looks like.
In order for the limit to exist we need both one-sided limits to exist.
As x approaches zero from the left, y gets close to 0 also, therefore
As x approaches zero from the right, y gets close to 1, therefore
Since the left-side limit is 0 and the right-side limit is 1, and 0 and 1 aren't the same,
does not exist.
We start by graphing f:
In order for the limit to exist we need both one-sided limits to exist and be identical.
As x approaches two from the left, y gets close to 5, therefore
As x approaches two from the right, y still gets close to 5, so
Since the left-hand limit and the right-hand limit both exist and are equal to 5,