借助Maple讨论y=x~αsin1/x(α∈R)的连续性

Discuss Continuity of y=x~αsin1/x(α∈R) with the Help of the Maple Software

借助Maple软件,对yn=xnsin 1/x(n=0,1,2,3)进行了分类比较、讨论,给出它们在x=0处及附近的部分分析性质的证明;作出十分直观的示意图,消除以前只能凭空想象的缺陷;并对y=xαsin 1/x(α∈R)和y=xαcos 1/x(α∈R)作了推广、引申;结合实际问题进行了应用讨论.

With the help of the Maple Software ,it compares, classifies and discusses on yn=x^nsin1/x（n=0,1,2,3） and provides by the identification of properties in x=0 and nearby, giving out a very ocular sketeh map, and overcomes the shortcoming of imagination in the past ;and has popularized, amplified y=x^αsin1/x（α∈R） and y=x^αcos1/x（α∈R）;Finally it discusses the application combining with the practical problems.