USING CLASSICAL ANALYSIS AND COMPUTER TECHNOLOGIES TO STUDY POWER-EXPONENTIAL TYPE EQUATIONS

Abstract

 In the present paper basing on properties of the power and the exponential functions we study power-exponential type equations and establish properties of their roots. Since such equations are transcendental there is no method to find exact roots. But using well known methods of classical calculus and tools of the system of analytical calculations Maple we can establish the boundaries of roots and predict their convergence as the degree tends to infinity. We also give qualitative and quantitative analysis of the difference between the power and the exponential functions for large values of the argument and suggest a convenient formula for approximate but fast calculations. Results of calculations demonstrated in tables and graphs were obtained using Maple program.