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 <carlos@math.albany.edu>
    This problem was contributed by a student. It is offered as it is with no warranty of any kind
    Last modified:Thu Mar 22 15:53:07 GMT-0500 (EST) 2001