##

Logarithms and exponentials.

The logarithms and the exponentials can be defined in many ways. Precise definitions and proofs are given in Appendix I (i.e. chapter logs-exp).

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