1.讨论下列函数的连续性:-|||-(1) (x,y)=tan ((x)^2+(y)^2) ;-|||-(2) (x,y)=[ x+y] ;-|||-(3) f(x,y)= { , yneq 0 0, y=0;

6.讨论下列函数的连续性:-|||-(1) (x,y)=dfrac ({x)^2-(y)^2}({x)^2+(y)^2}-|||-(2) (x,y)=dfrac

1.函数 (x+y,xy)=(x)^2+(y)^2-xy, 则 f(x,y)=

讨论下列函数的连续性:-|||-^2+(y)^2neq 0,-|||-f(x,y)= ) (y)^2ln ((x)^2+(y)^2) 0,=0;

设 (x+y,x-y)=2((x)^2+(y)^2)(e)^(x^2-{y)^2}, 则 _(x)(x,y)-(f)_(y)(x,y)= __

证明:函数-|||-f(x,y)= ((x)^2+(y)^2)sin dfrac (1)(sqrt {{x)^2+(y)^2}}, ^2+(y)^2neq 0,

设函数 (x,y)=1-dfrac (cos sqrt {{x)^2+(y)^2}}(tan ({x)^2+(y)^2)} ,则当定设函数 (x,y)=1-df

已知函数 z=f(x,y) 连续且满足 lim _(xarrow 1)dfrac (f(x,y)-x+2y+2)(sqrt {{(x-1))^2+(y)^2}}

设函数 y=y(x) 由方程 ^3+x(y)^2+(x)^2y+6=0 确定,设函数 y=y(x) 由方程 ^3+x(y)^2+(x)^2y+6=0 确定,

164 设f(x,y)有二阶连续偏导数, (x,y)=f((e)^xy,(x)^2+(y)^2), 且 f(x,y)=1-x-y+-|||-(sqrt ({(x

设f(x,y)= ^4+{y)^2},(x)^2+(y)^2neq 0 0,(x)^2+(y)^2=0 .处是否连续？设,试问在点处是否连续？