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Computing a Limit


*****

Problem:

Find the following limit, assuming that it exists.

> ;

                                              2  2
                                             x  y
                                 lim        -------
                            x, y -> (0, 0)   2    2
                                            x  + y


Solution:


If the limit exists then the function approaches the same value along any path to (0,0). In particular if we take y=x we obtain,

> Limit(`x^2*x^2`/`(x^2+x^2)`,x=0) = Limit(x^2*x^2/(x^2+x^2),x=0);

                               x^2*x^2                 2
                       lim    --------- =  lim    1/2 x  = 0
                      x -> 0  (x^2+x^2)   x -> 0

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Thu Mar 22 15:47:53 EST 2001