Evaluation of limits including integrals by L Hpitals rule

Abstract

Limit is significant concept in mathematic analysis. Technically, limits definition in mathematics is that a variable in a function gradually approximates to a certain value in the changing process which cannot be ended. L Hpitals rule and Taylor expansion, together with other methods such as Stolz theorem, are usually used in measuring a limits value. In this paper, it will focus on some representative limits that are related to definite integrals. L Hpitals rule and Taylor's expansion are also jointed used so as to solve the problems. The main part of this work talks about the limit of the integration of trigonometric function, under which situation Taylors expansion is commonly utilized. This article talks about the polynomials integration as well, under which situation the approximation method is also employed. Trigonometric function and polynomial function are frequently appeared in evaluating limit. This means that this paper is summarizing the prime functions in integration-related limits.