A relational database management system (RDBMS) optimizes limit queries over analytical functions, wherein the limit queries include an output clause comprising a LIMIT, TOP and SAMPLE clause with an expression specifying a limit that is a number K or a percentage α %. The optimizations of the limit queries include: (1) static compile-time optimizations, and (2) dynamic run-time optimizations, based on semantic properties of “granularity” and “input-to-output cardinality” for the analytical functions.