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Determine If Is Everywhere Continuous, and If Not, Locate the Point(s) of \begin{array}

question 237

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Determine if f(x,y)={x2+xyx2+y2 if (x,y)(0,0)1 if (x,y)=(0,0)f ( x , y ) = \left\{ \begin{array} { l l } \frac { x ^ { 2 } + x y } { x ^ { 2 } + y ^ { 2 } } & \text { if } ( x , y ) \neq ( 0,0 ) \\1 & \text { if } ( x , y ) = ( 0,0 )\end{array} \right. is everywhere continuous, and if not, locate the point(s) of discontinuity.


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