When does a problem in mathematics have no limit?

Answer 1

When the limit as the function approaches from the left, doesn't equal the limit as the function approaches from the right.

For example, let's look at the function 1/x as x approaches 0.

As it approaches 0 from the left, it travels towards negative infinity.

As it approaches 0 from the right, it travels towards positive infinity.

Therefore, the limit of the function as it approaches 0 does not exist.