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#1 2005-12-18 16:34:55

Ricky
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Registered: 2005-12-04
Posts: 3,791

Limits and multiple variables

Is there any easy way to show the limit of a non-continuous function, that is, besides doing an epsilon-delta proof?

For example, how would you show:

Last edited by Ricky (2005-12-18 16:38:39)


"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..."

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#2 2005-12-18 17:29:09

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Limits and multiple variables

I don't know better method, but here how I solve this:

,so we can proof it only for positive x and y and xy is positive so we can sqrt() it:
, but
but
and
, so
and

Last edited by krassi_holmz (2005-12-18 17:43:05)


IPBLE:  Increasing Performance By Lowering Expectations.

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#3 2005-12-18 18:17:11

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Limits and multiple variables

If you are able to reduce your limit to sum of non-multiple limits you can find them and then you can sumarize them.


IPBLE:  Increasing Performance By Lowering Expectations.

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#4 2005-12-18 18:19:03

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Limits and multiple variables

But it won't work in all ways: It can bring to something like that:

that is no null at all the cases.


IPBLE:  Increasing Performance By Lowering Expectations.

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#5 2005-12-18 18:20:35

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Limits and multiple variables


IPBLE:  Increasing Performance By Lowering Expectations.

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