判断高数二元函数是否连续x^2y/(x^2+y^2),x^2+y^2≠0f(x,y)=0 ,x^2+y^2=0问此函数在(0,0)处是否连续?等我有钱了再报答你,
2019-04-14
判断高数二元函数是否连续
x^2y/(x^2+y^2),x^2+y^2≠0
f(x,y)=
0 ,x^2+y^2=0
问此函数在(0,0)处是否连续?等我有钱了再报答你,
优质解答
f(x,y) = x^2y/(x^2+y^2),
0 ≤ | f(x,y) | = x²/(x²+y²) * |y| ≤ |y|
lim(x,y)->(0,0) |y| = 0,利用迫敛准则,
lim |f(x,y)| = 0,∴ lim f(x,y) = 0 = f(0,0)
故此函数在(0,0)处连续.
注：计算二重极限,不能取特殊路径.
f(x,y) = x^2y/(x^2+y^2),
0 ≤ | f(x,y) | = x²/(x²+y²) * |y| ≤ |y|
lim(x,y)->(0,0) |y| = 0,利用迫敛准则,
lim |f(x,y)| = 0,∴ lim f(x,y) = 0 = f(0,0)
故此函数在(0,0)处连续.
注：计算二重极限,不能取特殊路径.