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March 26th, 2017, 01:44 AM   #1
ZMD
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Directional Derivative and Totally Differentiable

How to show the following:

Show that the function:
f(x,y) =
(x^3- y^3)/(x^2 +y^2) , (x,y) not equal to (0,0)
0, (x,y)=(0,0)

has directional vector at (0,0) but not totally differentiable at (0,0)
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March 27th, 2017, 06:32 AM   #2
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del f=f$\displaystyle _{x}$i + f$\displaystyle _{y}$j

ck f$\displaystyle _{xy}$ = f$\displaystyle _{yx}$

at (0,0)
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