The scenario can be described using a piecewise function like:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
<h3>When the value exists but the limit does not?</h3>
Remember that the limit only exists if the limit from left and the limit from the right give the same value.
Then, we can just define a piecewise function of the form:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
Clearly, this is not a continuous function.
Notice that:
So the limits from left and right are different, then:
Does not exist.
If you want to learn more about limits:
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