  In this paper, using the Maclaurin series of the functions $(1+x)^{1/x}$,
some inequalities from papers Bicheng Debnath [1998] and Mortici Jang [2015]
are generalized. For arbitrary Maclaurin series some general limits of Keller's
type are defined and applying for generalization of some well known results.

Classical Analysis and ODEs