Calc III Question ?

 Show that the following limit does not exist. ``` 4 4 x y lim ---------- x, y -> (0, 0) 2 4 3 (x + y ) ``` The limit does not exist because: the paths y=ax produce limits that depend on a. The paths y=x and x=y^2 produce limits 0 and infinity respectively. The paths y=x and x=y^2 produce limits 0 and 1/8 respectively. The paths y=x produce different right and left limits as x->0. By L'Hopital's rule the limit along the path y=x does not exist.

Carlos Rodriguez <carlos@math.albany.edu>
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