Place the factorial function into a standard limit notation. For example, f (x) = 3 / (x! - 5), placed into limit notation, becomes lim x -> ∞ 3 / (x! - 5). Read this as, "The limit as x approaches infinity of 3 / (x! - 5)."
Evaluate the values the function takes on as "x" becomes larger in its approach toward infinity. In this example, as "x" becomes arbitrarily large, the expression 3 / (x! - 5) becomes increasingly small. This is because any number divided by increasingly growing numbers gets smaller.
Solve the limit with the value determined in Step 2. In this case, lim x -> ∞ 3 / (x! - 5) approaches 0 as "x" grows larger toward infinity; therefore, the limit is equal to 0.