Suppose that there exists a linear function $L ( x , y )$ near the point (0,0)such that the difference between $f ( x , y )$ and $L ( x , y )$ approaches 0 as $( x , y )$ approaches (0,0).Then f is differentiable at (0,0)with $L ( x , y )$ as its local linearization.

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The Answer of Suppose that there exists a linear function $L ( x , y )$ near the point (0,0)such that the difference between $f ( x , y )$ and $L ( x , y )$ approaches 0 as $( x , y )$ approaches (0,0).Then f is differentiable at (0,0)with $L ( x , y )$ as its local linearization.

Suppose That There Exists a Linear Function L(x,y)L ( x , y )L(x,y)

Suppose That There Exists a Linear Function $L ( x , y )$