【摘要】 利用泰勒展开式,把分段函数在以x0为分段点的相邻区间上展开为(x-x0)的泰勒级数,然后通过观察和比较相邻分段区间上泰勒展开式中的k阶系数是否对应相等,来判断分段函数在x=x0点是否存在k阶导数.更多还原

【Abstract】 Using Taylor expansion,a piecewise-defined function can be expanded as power series of(x-x0) in a neighborhood of x0,one for x>x0 and the other for x<x0.By comparing the corresponding Taylor coefficients we can establish criteria for the existence of higher derivatives of the function at x=x0.更多还原