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You are not logged in. #1 20060303 08:44:47
Limit questionIn studying the limits of multivariable functions, is it reliable to use y=mx and y=x^2 to evaluate the limit of f(x,y) ? Why do we use only these two anyway? And what does a "level curve" mean? "Fundamentally one will never be able to renounce abstraction." Werner Heisenberg #2 20060303 14:03:56
Re: Limit questionYes and no. By using these two, you are usually going to be showing that the limit does not exist. So you want to end up with is two limits not being equal. Last edited by Ricky (20060303 14:04:12) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060303 21:23:53
Re: Limit questionCan't you use y=x+k too? IPBLE: Increasing Performance By Lowering Expectations. #4 20060303 21:26:18
Re: Limit questionThanks for your explanation, I think I have a better understanding now. But suppose I'm finding the limit of a function f(x,y) and I substitue y=mx and end up with the limit = m . Can I stop here and conclude that the limit does not exist simply because it's a variable ? "Fundamentally one will never be able to renounce abstraction." Werner Heisenberg #5 20060303 21:38:45
Re: Limit questionCan you give some example, please? IPBLE: Increasing Performance By Lowering Expectations. #6 20060303 23:17:15
Re: Limit questionSure thing krassi_holmz, "Fundamentally one will never be able to renounce abstraction." Werner Heisenberg #7 20060303 23:27:33
Re: Limit questionRicky, but notice that if I use y=0 for f(x,y) = yx^2 / ( x^4  2yx^2 + 3y^2 ) , the limit will be 0. "Fundamentally one will never be able to renounce abstraction." Werner Heisenberg #8 20060304 07:02:13
Re: Limit questionHere's a plot of this function: Last edited by krassi_holmz (20060304 07:08:35) IPBLE: Increasing Performance By Lowering Expectations. #9 20060304 07:11:59
Re: Limit questionSorry for the colors. IPBLE: Increasing Performance By Lowering Expectations. #10 20060304 10:56:47
Re: Limit questionChemist, nothing is going to work for all functions. But (x,0) and (x,x) work for a whole lot, and they are easy. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 