When evaluating limits, if the numerator is zero and the denominator is non-zero, the limit approaches zero, as shown by lim x-> a (0/x) = 0 and lim x-> +/- infinity (0/x) = 0. However, if both the numerator and denominator approach zero, the limit becomes indeterminate, potentially resulting in any real number or infinity. This distinction is crucial in calculus when analyzing limits involving rational expressions. Understanding these principles helps clarify the behavior of functions as they approach specific points or infinity. Thus, limits involving zero in the numerator require careful consideration of the denominator's behavior.