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"?

Question

Mathematics

Marie Mayo

26 February, 22:07

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"?

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Lou · 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.