LIMIT INTERCHANGE IN INTEGRATION AND SUMMATION BY USING L’HOSPITAL’S RULE - R.A., KHAKRE (Innovare Journal of Sciences, 2020)
Abstract : It is known that L’Hospital’s Rule is one of the important results used for obtaining the limits of those functions which are of the type at a given point ‘a’ where may take an indeterminate form like, , or. The main purpose of this paper is to illustrate some problems and results in advanced calculus with the help of this rule and examples .we shall show that there are some sequences of functions for which the integral of the limit is equal to limit of the integral .We also illustrate through examples the L’Hospital’s Rule fails in the limit interchange process if a sequence under consideration is not uniformly convergent.