As an application, let us compute the limit, if it exists, of for arbitrary large. Note that we have here a situation of the type described above in subsection subsubsection Numerator and denominator have both an infinite limit.
As and , we have: .
Note that there are other ways to solve this question; one of them will appear with L'Hopital's rule (Theorem L'Hopital), another one with Taylor polynomials (v.i. Def. Taylor polynomials).
Noah Dana-Picard 2007-12-28