显然连续.由于limf(x,0)=limf(0,y)=0 故偏导数存在
|[f(x,y)-f(0,0)]/ρ|
=lim|xysin(1/ρ)/ρ|
≤lim[xy/ρ|
≤lm√xy/2=0
故可微
高数题一枚!速求,本人巨菜,恳请大家耐心讲解
显然连续.由于limf(x,0)=limf(0,y)=0 故偏导数存在
|[f(x,y)-f(0,0)]/ρ|
=lim|xysin(1/ρ)/ρ|
≤lim[xy/ρ|
≤lm√xy/2=0
故可微