I'm searching to perform this kind of limit (without restricting and executing the limit to a variable):
$$ \lim_{(x, y)\to(0, 0)}\frac{x^3y}{x^6+y^2} $$ In the documentation I didn't find a multivariate limit function..
This smells of homework, so I'll just submit a simple suggestion : you may find inspiration (but not necessarily a solution) in this book (pp.91-2).
Hoping that this may incite you to read the rest of this (excellen)t book...
The problems are :
As far as I can tell, you didn't say a word about an integral ; and
while Sage will happily tell you :
sage: var("y") y sage: (x^3*y/(x^6+y^2)).limit(y=0).limit(x=0) 0
This is a result of a "mechanical" computation, with no attempt to prove the its validity. Sage may however give you a hint:
sage: var("x,y,r,theta")
(x, y, r, theta)
sage: f(x,y)=x^3*y/(x^6+y^2)
sage: g(r,theta)=f(x,y).subs({x:r*cos(theta),y:r*sin(theta)})
sage: parametric_plot3d([r*cos(theta),r*sin(theta),g(r,theta)],(r,0,1/20),(theta,0,2*pi))
What's this "hole" ? (Hint : not as easy as analysing as it seems...).
Computing isn't enough : you have to think...
Asked: 2020-09-05 11:14:41 +0100
Seen: 497 times
Last updated: Sep 05 '20
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