TITLE: Show that limit DNE
# !b2 Problem:
Show that the following limit DNE (Does Not Exist):
> ;
                                             2
                                            x  + y
                                 lim        -------
                            x, y -> (0, 0)   2    2
                                            x  + y

# !b3 Solution:
Consider paths of the form y=a x^m with m>0 as x->0.
> Limit('(x^2+a*x^m)/(x^2+a^2*x^(2*m))',x=0) = 
> limit((1+a*x^(m-2))/(1+a^2*x^(2*m-2)),x=0);
                         2      m                      (m - 2)
                        x  + a x                1 + a x
               lim    -------------- =  lim    -----------------
              x -> 0   2    2  (2 m)   x -> 0       2  (2 m - 2)
                      x  + a  x                1 + a  x

# and for m=2 we get this limit to be 1+a. This depends on a so
the limit DNE.

>