An equivalent infinitesimal substitution problem of indeterminate limit from a literature and its correction

This article delves into the complexities of indeterminate limits and the pivotal role of infinitesimal substitution in their resolution. Within the realm of mathematical analysis, indeterminate limits--characterized by expressions such as "0/0" and "∞/∞"--pose a significant challenge to traditional limit computation techniques. Equivalent infinitesimal substitution is applied to reduce the difficulty of calculation in solving indeterminate limit problems. However, the substitution cannot be directly applied to indeterminate infinitesimal subtraction and addition. This paper points out the problem of equivalent infinitesimal substitution in the indeterminate limit calculation which includes addition and subtraction used in many papers, and amends the infinitesimal substitution theorem given in the papers.