The paper discusses differentiability and continity of a class of piecewise functions at piecewise point the continuity and the continuity of a class of piecewise function at the point of subsection by the application of the Taylor for‐mula and the derivative limit theorem ,and carries on the promotion ,and gets better results .%通过应用Taylor公式及导数极限定理,对一类分段函数在分段点处的可导性及连续性展开探讨,并进行推广,得到较好的结果。
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