来自黄攀峰的问题
设f(x)=xarctan1x2,x≠00,x=0,试讨论f′(x)在x=0处的连续性.
设f(x)=
xarctan1x2 , x≠00 , x=0,试讨论f′(x)在x=0处的连续性.
1回答
2020-05-15 14:18
设f(x)=xarctan1x2,x≠00,x=0,试讨论f′(x)在x=0处的连续性.
设f(x)=
xarctan1x2 , x≠00 , x=0,试讨论f′(x)在x=0处的连续性.
∵x≠0时,f′(x)=(xarctan1x2)′=arctan1x2+x(arctan1x2)′=arctan1x2+x•11+1x4•(1x2)′=arctan1x2+x•11+11+x4•−2xx4=arctan1x2−2x21+x4x=0时,f′(0)=limx→0f(x)−f(0)x=limx→0xarctan1x2x=limx→0arct...