My Math Forum How do I prove this multivariable limit problem?

 Calculus Calculus Math Forum

 May 9th, 2014, 09:01 PM #1 Newbie   Joined: Apr 2014 From: California Posts: 10 Thanks: 3 How do I prove this multivariable limit problem? Compute $\displaystyle \lim_{x,y\to (0,0)}$ $\displaystyle 3xy\over x^2+y^3$ along lines of the form $\displaystyle y=mx$, for $\displaystyle m \neq 0$. What can you conclude? When I do it, I end up with 3m which is a limit. I know the function is discontinuous at (0,0) but I don't know how to prove it.
May 9th, 2014, 09:26 PM   #2
Math Team

Joined: Dec 2013
From: Colombia

Posts: 7,683
Thanks: 2664

Math Focus: Mainly analysis and algebra
Quote:
 Originally Posted by RedBarchetta I end up with 3m
The thing about that answer is that you get a different limit for every direction of approach to (0, 0). When when dealing with a single-variable limit, that means that the limit doesn't exist (or is a pair of one-sided limits).

Actually, I get $\frac{3m}{1 + m^2}$ (valid for all $m$) by that approach, but the problem I identified before still applies.

 Tags limit, multivariable, problem, prove

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post maluita659 Calculus 7 February 15th, 2014 01:15 PM lesaltersvi Real Analysis 2 February 22nd, 2013 04:47 AM Robertinho! Linear Algebra 1 September 29th, 2011 12:31 PM tmlfan_179027 Calculus 3 October 4th, 2010 10:06 AM person1200 Calculus 2 August 29th, 2010 10:19 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top