Question

讨论函数的连续性与可导性

讨论f(x)=|sinx|在x=0处的连续性与可导性

Answer 1

x→0+
lim |sinx| =lim sinx =0 =sin 0
x→0-
lim sinx = lim -sinx =0 =sin 0
左右都连续。所以连续

x→0+
lim (|sinx|-|sin0)|/(x-0) =lim sinx/x =1
x→0-
lim (|sinx|-|sin0)|/(x-0) = lim -sinx/x =-1

左右导数不等，所以不可导