Question

For some piecewise function f(x), the limit as x approaches "a" from the left is 5. The limit as x approaches "a" from the right is -3. What is the limit of f(x) as x approaches "a"?

Answer 1

Answer: The limit does not exist.

Step-by-step explanation: The limit of a piecewise function f(x) as it approaches "a" will exist if and only if the value of the limit of f(x) as x approaches "a" from the left is the same with the value of the limit of f(x) as x approaches "a" from the right.

From the given question the value are not the same. We have 5 (limit from the left) and -3 (limit from the right). So, we can conclude that the limit of f(x) as x approaches "a" does not exist.