The given functions limx→1−f(x)=3 and limx→1+f(x)=7, explain what it means and state if its possible that limx→1 exists.
The meaning of these limits is that as x
approaches 1 from the negative side, the limit of the graph
goes towards a y-value of 3. On the other hand, if we consider x that approaches 1 from
the positive side, the limit of the graph goes towards a y-value of 7.
It is not possible that limx→1 exists because as stated in the definition, limx→af(x)=L if and
only if limx→a−f(x)=L and limx→a+f(x)=L.
The limit of the function as x approaches 1 does not exist because the values are different as x
approaches 1 from left and right.
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