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lim(x,y)→(0,0)x2−y2x2+y2\displaystyle \lim_{(x, y) \to (0, 0)} \frac {x^2 - y^2}{x^2 + y^2}(x,y)→(0,0)limx2+y2x2−y2
x, y = var('x,y') plot3d((x^2 - y^2)/(x^2 + y^2), (x,-4,4), (y,-4,4), aspect_ratio=1)
lim(x,y)→(0,0)xyx2+y2\displaystyle \lim_{(x, y) \to (0, 0)} \frac {xy}{x^2 + y^2}(x,y)→(0,0)limx2+y2xy
x, y = var('x,y') plot3d((x*y)/(x^2 + y^2), (x,-4,4), (y,-4,4), aspect_ratio=1)
lim(x,y)→(0,0)3x2yx2+y2=0\displaystyle \lim_{(x, y) \to (0, 0)} \frac {3x^2y}{x^2 + y^2} = 0(x,y)→(0,0)limx2+y23x2y=0
x, y = var('x,y') plot3d((3*x^2*y)/(x^2 + y^2), (x,-4,4), (y,-4,4), aspect_ratio=1)
