Find Two Paths of Approach from Which One Can Conclude $f \left( x _ { 0 } , y _ { 0 } \right) = - 2$

question 288

Essay

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
-If $f \left( x _ { 0 } , y _ { 0 } \right) = - 2$ and the limit of $f ( x , y )$ exists as $( x , y )$ approaches $\left( x _ { 0 } , y _ { 0 } \right)$ , what can you say about the continuity of $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$ at the point $\left( \mathrm { x } _ { 0 } , \mathrm { y } _ { 0 } \right)$ ? Give reasons for your answer.

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