Left and right limits can define the concept of left and right derivatives. The left limit means that the independent variable X approaches x0 from the side less than x0 and from the left on the number axis. You can also define the concept that the right limit approaches x0 from the right. However, the concept of limit does not specify which specific direction to approach x0, so the existence of limit requires that both left and right limits exist and be equal. The derivative is defined by the limit, and the difference between the left and right limits here means that the left and right derivatives are different, which means that the derivative does not exist.