if lim x->a+ f(x) =/= lim x->a- f(x) then…
lim x->a f(x) doesn’t exist
If the limit of the function f(x) from the right side as x approaches a is not equal to the limit of the function from the left side as x approaches a, then the limit of the function as x approaches a does not exist.
In mathematical notation, we can express this as:
lim x->a f(x) DNE (does not exist)
This can also be written as:
lim x->a- f(x) =/= lim x->a+ f(x)
This is because the limit of a function at a point is dependent on the values that the function takes as x approaches that point from both the left and right sides. If the function approaches different values from the left and right sides, then it cannot have a well-defined limit at that point.
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