Mathematica实现函数间断点的可视化

Study on Visualization of Function Discontinuous Points by Mathematica

用Mathematica软件的系统函数Plot所绘制的函数图形中,在间断点处的单侧连续性没有体现出来。本研究使用Mathematica所提供的模式替换、方程求解等功能,实现了自动识别分段函数中的所有分段点,并对每个分段点计算左右极限及函数值,从而实现了分段函数图形中每一个间断点处单侧连续性的可视化。

In the graph of function made by Plot in Mathematica, the single side continuousness at discontinuous points cannot be visual. In this paper, the automatic recognization of all dividing points in piecewise function and calculation of its left and fight limits as well as the function value were successfully actualized by utilizing the functions of Mathematica, such as pattern replacing and equation solution. Therefore the visualization of the single side continuousness at each discontinuous point in the graph of piecewise function was achieved.