TITLE: limit of $\frac{2xy^3}{7x^2+4y^6}$, different answers.
QUESTION [5 upvotes]: Good evening, everyone I've tried my possible best to evaluate the limit as $(x,y) \to (0,0)$ but Using sage the answer is 0 either ways but one textbook is saying the limit doesn't exist.  Could the 2 answers be correct?

REPLY [2 votes]: The Wolfram|Alpha result is indeed a weakness (bug).
In slightly more detail, which I hope I won't have to regret, the underlying problem is in Mathematica's Limit handling of intervals.
ee = (rho*Interval[{-1, 1}])/(rho^2*Interval[{-1, 1}] + 
     Interval[{-1, 1}]);
In[63]:= Limit[ee, rho -> 0]
This incorrectly gives zero when it should return unevaluated.
This is a known bug. What's not known at this point is how to fix it.