17/12/11 09:18:39.83 iFFP4S+k.net
>>653
f(x, y) = x*y*(x^2 - y^2) / (x^2 + y^2)
| ∂f(x, y) / ∂x |
=
| y | * | 1 + [2*y^2 / (x^2 + y^2)] * [1 - 2*y^2 / (x^2 + y^2)] |
≦
| y | * ( 1 + [2*y^2 / (x^2 + y^2)] * | 1 - 2*y^2 / (x^2 + y^2)] |
0 < y^2 / (x^2 + y^2) ≦ 1
だから
| y | * ( 1 + [2*y^2 / (x^2 + y^2)] * | 1 - 2*y^2 / (x^2 + y^2)] |
≦
| y | * ( 1 + [2*y^2 / (x^2 + y^2)]
≦
| y | * ( 1 + 2)
=
3 * |y|
≦
3 * sqrt(x^2 + y^2)