二元函数的间断点（1）f(x,y)=(x-y)/(x-y^2)(2)f(x,y)=sin{1/(x+y+1)}都是求间断点

Question

二元函数的间断点
（1）f(x,y)=(x-y)/(x-y^2)
(2)f(x,y)=sin{1/(x+y+1)}
都是求间断点

Answer 1

(1)
f(x,y)=(x-y)/(x-y^2)
间断点
x-y^2 =0
x = y^2
间断点 = { (a^2,a) | a∈R}
(2)
f(x,y)=sin{1/(x+y+1)}
间断点
x+y=1 =0
x = 1-y
间断点 = { (1-b,b)| ba∈R}