Let Does This Function Have a Limit at the Origin?
If

question 59

Essay

Let $$f ( x , y ) = \left\{ \begin{array} { l l } \frac { x ^ { 4 } + y ^ { 4 } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } & \text { if } ( x , y ) \neq ( 0,0 ) \\0 & \text { if } ( x , y ) = ( 0,0 )\end{array} \right.$$ Does this function have a limit at the origin?
If so, prove it. If not, demonstrate why not.

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