函数单调性的一个判别法及应用

摘要

三角不等式是一种常见类型的不等式，通常包含sinx， tanx等无穷小（当x→0时），以及两个无穷小之比。本文提出两个无穷小之比单调性判别法，判别某些函数的单调性以及证明一些三角不等式。%The triangle inequality is a common type of inequality , usually contains infinitesimal , such as sinx, tanx (x→0), and the ratio of two infinitely small quantities.A distinction law of the monotony of the ratio of two infinitely small quantities is proposed to determine the monotonicity of certain functions and prove certain triangle inequalities .