Friday, January 18, 2019

Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 2

The given functions limx1f(x)=3 and limx1+f(x)=7, explain what it means and state if its possible that limx1 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 limx1 exists because as stated in the definition, limxaf(x)=L if and
only if limxaf(x)=L and limxa+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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