The limit of SQRT(X)SIN(1/X) as X approaches infinity can be evaluated using the squeeze theorem. By substituting 1/X with y, the limit transforms to lim y→0 of (sin y)/y, which equals 1. Additionally, it is established that sin(1/X) is bounded above by 1/X, leading to the conclusion that the limit approaches 0. The discussion emphasizes the importance of inequalities and the squeeze theorem in proving the limit's behavior. Overall, the limit of SQRT(X)SIN(1/X) as X goes to infinity is confirmed to be 0.