Question

For a two sided limit to exist, what conditions must be met?

1) Both the limit from the left and the limit from the right must exist
2) Both the limit from the left and the limit from the right must be equal to a real number
3) The limit cannot equal infinity
4) All of the above

Answer 1

To have a two-sided limit exist, the left and right limits must both exist, be equal to a real number, and not equal infinity.

Step-by-step explanation:

To have a two-sided limit exist, the following conditions must be met:

1. Both the limit from the left and the limit from the right must exist: This means that as the input values approach the point in question from the left and the right, the function must approach a specific value.
2. Both the limit from the left and the limit from the right must be equal to a real number: The left and right limits should approach the same value in order for the two-sided limit to exist.
3. The limit cannot equal infinity: The function should not approach infinity as the input values approach the point in question.

Therefore, the correct answer is 3) The limit cannot equal infinity.