| exists if and only if is continuous on the immediate left of , i.e., there exists such that is continuous on . Here, "continuous" means that the two-sided limit at every point in the open interval equals the value of the function. |
| exists implies that is continuous on the immediate left of , i.e., there exists such that is continuous on . Here, "continuous" means that the two-sided limit at every point in the open interval equals the value of the function. However, the converse implication does not hold. |
| exists if is continuous on the immediate left of , i.e., there exists such that is continuous on . Here, "continuous" means that the two-sided limit at every point in the open interval equals the value of the function. However, the converse implication does not hold. |
| Neither of the conditions " exists" and " is continuous on the immediate left of " imply one another. |