Question

Describe a scenario where the function value exists at x=c, but the limit does not exist.

Answer 1

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.

When the value exists but the limit does not?

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:

$f(c) = c.\\\\ \lim_{x \to c^{-}} f(x) = 1/c\\\\ \lim_{x \to c^{+}} f(x) = 1/(c + 73)$

So the limits from left and right are different, then:

$\lim_{x \to c^{}} f(x)$

Does not exist.

If you want to learn more about limits:

brainly.com/question/5313449

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