Determine the implied limit argument value. For example, a limit function such as, lim x -> ∞ Sin (pi / x), spoken as "the limit as 'x' approaches infinity of the sine of pi over 'x'," requires that the internal argument, pi / x in this case, be evaluated at pi / ∞ before the sine function is performed. In this case, the value as x -> ∞ is equal to 0. It is important to remember that limits are not concerned with the value at the limit, but rather the value that is approached as the value of "x" grows closer to that limit.
Substitute the derived limit argument value into the inner function. This changes lim x -> ∞ sin (pi / x) to sin (0).
Evaluate the inner function of the limit function, in this case the sine function, at the previously determined value. Concluding the example, sin (0) = 1.