File:Continuous Functions – Non-continuous 2d-example (view 2).svg
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![File:Continuous Functions – Non-continuous 2d-example (view 2).svg](https://upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Continuous_Functions_%E2%80%93_Non-continuous_2d-example_%28view_2%29.svg/512px-Continuous_Functions_%E2%80%93_Non-continuous_2d-example_%28view_2%29.svg.png?20130214222433)
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[edit]DescriptionContinuous Functions – Non-continuous 2d-example (view 2).svg |
English: The function f: R²→R, f(x,y)=f(0,0):=0 for x=y=0 and f(x,y):=xy/(x²+y²) otherwise, is not continuous in (0,0), despite f_y: R→R, f_y(x):=f(x,y) for any fixed y is continuous just as is f_x: R→R, f_x(y):=f(x,y) for any fixed x. Deutsch: Die Funktion f: R²→R, f(x,y)=f(0,0):=0 für x=y=0 und f(x,y):=xy/(x²+y²) andernfalls, ist nicht stetig im Punkt (0,0), obwohl für beliebiges festes y f_y: R→R, f_y(x):=f(x,y) stetig ist wie auch für beliebiges festes x f_x: R→R, f_x(y):=f(x,y). |
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Author | Xantares |
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current | 22:24, 14 February 2013 | ![]() | 512 × 512 (597 KB) | Xantares (talk | contribs) | User created page with UploadWizard |
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