Let \(f\left( {x,y} \right) = \;\left\{ {\begin{array}{*{20}{c}} {\frac{{xy}}{{\sqrt {{x^2} + {y^2}} }}\;\;\;{x^2} + {y^2} \ne 0}\\ {0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x = y = 0} \end{array}} \right.\), Then

f(x, y) is continuous at the origin

f(x, y) is not differentiable at the origin

Let \(f\left( {x,y} \right) = \;\left\{ {\begin{array}{*{20}{c}} {\fr

1.	Let \(f\left( {x,y} \right) = \;\left\{ {\begin{array}{*{20}{c}} {\frac{{xy}}{{\sqrt {{x^2} + {y^2}} }}\;\;\;{x^2} + {y^2} \ne 0}\\ {0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x = y = 0} \end{array}} \right.\), Then
A.	f(x, y) is not differentiable at the origin
B.	f(x, y) is continuous at the origin
C.	fx (0,0) = f(0,0)
D.	fy (0,0) = f(0,0)
Answer» B. f(x, y) is continuous at the origin

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Let \(f\left( {x,y} \right) = \;\left\{ {\begin{array}{*{20}{c}} {\frac{{xy}}{{\sqrt {{x^2} + {y^2}} }}\;\;\;{x^2} + {y^2} \ne 0}\\ {0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x = y = 0} \end{array}} \right.\), Then

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