Evaluate the limit of a piecewise function

The video tutorial explains how to determine the limit of a function as X approaches zero. It emphasizes that for a limit to exist, the left-hand and right-hand limits must be equal. The tutorial demonstrates calculating these limits using the functions X^3 and sqrt(X) and shows that direct substitution can be used since both functions are continuous. The conclusion is that the limit is zero as both sides approach zero.

How do you determine if two functions are continuous at a point?

What conclusion can be drawn about the limit as X approaches zero from both sides?