ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 06 Sep 2020 02:36:38 +0200I'm searching to perform this multivariate limit (correctly)https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/ 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..Sat, 05 Sep 2020 11:14:41 +0200https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/Answer by Emmanuel Charpentier for <p>I'm searching to perform this kind of limit (without restricting and executing the limit to a variable):</p>
<p>$$
\lim_{(x, y)\to(0, 0)}\frac{x^3y}{x^6+y^2}
$$
In the documentation I didn't find a multivariate limit function..</p>
https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?answer=53318#post-id-53318This smells of homework, so I'll just submit a simple suggestion : you may find *inspiration* (but not necessarily a solution)
in [this book](http://sagebook.gforge.inria.fr/english.html) (pp.91-2).
Hoping that this may incite you to read the rest of this (excellen)t book...Sat, 05 Sep 2020 16:33:24 +0200https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?answer=53318#post-id-53318Comment by Teo7 for <p>This smells of homework, so I'll just submit a simple suggestion : you may find <em>inspiration</em> (but not necessarily a solution)
in <a href="http://sagebook.gforge.inria.fr/english.html">this book</a> (pp.91-2).</p>
<p>Hoping that this may incite you to read the rest of this (excellen)t book...</p>
https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?comment=53332#post-id-53332Got it, you've been very helpful.
ps I wanted to write "limits", but I was solving integrals at that time ...Sun, 06 Sep 2020 02:36:38 +0200https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?comment=53332#post-id-53332Comment by Teo7 for <p>This smells of homework, so I'll just submit a simple suggestion : you may find <em>inspiration</em> (but not necessarily a solution)
in <a href="http://sagebook.gforge.inria.fr/english.html">this book</a> (pp.91-2).</p>
<p>Hoping that this may incite you to read the rest of this (excellen)t book...</p>
https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?comment=53320#post-id-53320OK thanks. The problem is that I know how to perform this type of integrals, I just need a tool that gives me confirmation of the goodness of the resultsSat, 05 Sep 2020 18:39:17 +0200https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?comment=53320#post-id-53320Comment by Emmanuel Charpentier for <p>This smells of homework, so I'll just submit a simple suggestion : you may find <em>inspiration</em> (but not necessarily a solution)
in <a href="http://sagebook.gforge.inria.fr/english.html">this book</a> (pp.91-2).</p>
<p>Hoping that this may incite you to read the rest of this (excellen)t book...</p>
https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?comment=53331#post-id-53331The 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*...Sat, 05 Sep 2020 22:22:56 +0200https://ask.sagemath.org/question/53309/im-searching-to-perform-this-multivariate-limit-correctly/?comment=53331#post-id-53331