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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

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

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