The purpose of the paper is an alternative way of obtaining of the standard limits in the elementary theory of limits. The approach uses two double inequalities xe^-x ≤ sin x ≤ xe^x and xe^-x ≤ shx ≤ xe^x and the limit ...

The purpose of the paper is an alternative way of obtaining of the fundamental limits in the elementary theory of limits. The approach uses two double inequalities. The method is applied to the both limits simultaneously, that ...

The paper suggests three types of the necessary tests for the convergence of numerical series with positive terms. It is shown that these tests are consequences of the limit test of comparison with respect to the ...

The report describes the derivation and application of Mironenko’s test for series with positive terms. Mironenko’s test has the same limitations that have d'Alembert's ratio test and Cauchy's radical test. But in practical ...

In the paper it is shown that D’alembert’s test and Cauchy’s radical test are not independent one from another. It is proposed a transition scheme from one test to another and vice versa. The equivalence of the tests is ...