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Multivariable CalculusHardPartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Hard problem

Find the value of the constant aa for which f(x,y)=a xyx2+y2f(x,y) = \dfrac{a\,xy}{x^{2}+y^{2}} (for (x,y)≠(0,0)(x,y)\ne(0,0), with f(0,0)=0f(0,0)=0) is continuous at the origin.