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.
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Carlos Rodriguez <email@example.com>
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Last modified:Thu Mar 22 15:53:07 GMT-0500 (EST) 2001