※ 引述《rebe212296 (绿豆冰)》之铭言：
: 1.
: Let f:R^2→R be defined by f(x,y)=√|xy| for all (x.y)属于R^2
: Show that f_x and f_y both exist on R^2 and continuous on R^2\{(0,0)}
: but f is not differentable at (0,0).
: 2.
: Let f:R^2→R be defined by f(x,y)=[xy(x^2-y^2)]/(x^2+y^2) if(x,y)≠(0,0)
: and f(x,y) = 0 if(x,y)=(0,0)
: Show that f_xy(0,0) and f_yx(0,0) both exist but are not equal.
: 请问以上两题怎么解? 谢谢!
f(x,0) - f(0,0)
2. f (0,0) = lim