[分析] differentiable(2)

[suzzdicon (舒玆迪控)]

                   2
Find a function f:R -> R that is differentiable at each point

but whose partials are not continuous at (0,0)

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◆ From: 163.21.235.247
推 yusd24      :trying (x^2+y^2)sin(1/(x^2+y^2))
→ suzzdicon   :if (x,y)=(0,0) ???
推 yusd24      :sorry sin 裡面要開根號,  (0,0)的時候是零
→ suzzdicon   :我試試看 謝謝
→ suzzdicon   :f is differentiable at each point 如何證...?
推 math1209    :你只要知道單變數的情況就可以很快推到多變數.
→ math1209    :命 f(x) 是單變數情況,  則 f(x) + f(y) 會是你要的
→ math1209    :例子.