This is a piecewise or discontinuous function, so you can see it all as one function broken into two.
The limit is simply the result of f(x) or your 'y' value you get as you approach that value in x.
So as x approaches 0, the limit is 1.
As x approaches 2, the limit is 0.
The reason why the limit is 0 for the second one is because limits can either be reached or diverge, but it is allowed to be an exact output that lies on the graph, and that is the y-value or f(x) value at that point.
Timothy D.
tutor
Good catch, I forgot about that rule. I am still sure as x approaches 2, the limit is zero.
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02/22/22
Andrew F.
no limit as x approaches 0 due to "non-agreement" from right and left of zero--the limit does not exist if the "left-hand limit" does not equal the "right-hand limit"02/22/22