On 13 Apr., 21:04, Hector <hector1...@gmail.com> wrote: > On Wed, Apr 13, 2011 at 11:37 PM, Tom Bachmann <ness...@googlemail.com>wrote: > > > How do you plan on implementing limits of bivariate functions? > > Computing them is a *very* nontrivial extension over univariate limits > > (as far as I can tell) ... > > To find limit at (x,y) = (0,0) replace "y" by "mx" and check whether the > given limit is independent of "m" or not. If it is independent, than limit > exists and otherwise not.
No, this is *not* the definition. limit f(x,y) as (x,y)->(0,0) = a iff for all e > 0 there exists d > 0 s.t. x^2+y^2 < d ==> |f(x,y) - a| < e. As a counterexample, let f(x,y) = 0 if y <= 0 or x < 0, or x > 0 and y > exp(-1/x), and f(x,y) = 1 otherwise [so that f(x,y) is zero unless (x,y) is in the first quadrant und the graph of exp(-1/x)]. Then for all m, limit f(x,mx) = 0. But limit f(x,y) does not exist. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
