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Question Number 132477 by KZ last updated on 14/Feb/21

d e f i n e

f (x . y) =

{\frac{xy (x^{2} - y^{2})}{x^{2} + y^{2}} i f (x . y) \neq) 0.0)

0 i f (x . y) = (0.0)

s h o w t h a t f, \frac{\partial f}{\partial x} a n d \frac{\partial f}{\partial y} a r e

c o n t i n u o u s o n R^{2}

s h o w t h a t \frac{\partial^{2} f}{\partial x \partial y} a n d \frac{\partial^{2} f}{\partial y \partial x} e x i s t

o n R^{2} a n d a r e c o n t i n u o u s o n

R^{2} ∖ {0.0}

s h o w t h a t \frac{\partial^{2} f}{\partial x \partial y} = 1 \neq - 1 = \frac{\partial^{2} f}{\partial y \partial x}

Answered by guyyy last updated on 20/Feb/21

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