Use an proof to show that

So we need to prove that if then

However I do not know where to go from here, I can not seem to manipulate the and relate it with with any inequalities.

Thank you all!

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- August 15th 2010, 10:26 AMusagi_killerEpsilon-delta proof
Use an proof to show that

So we need to prove that if then

However I do not know where to go from here, I can not seem to manipulate the and relate it with with any inequalities.

Thank you all! - August 15th 2010, 02:03 PMVlasev
I think you should use start with the fact that [LaTeX ERROR: Convert failed] .

- August 16th 2010, 02:15 AMusagi_killer
Thanks for that, I've played around with that however I still can not seem to get it :(

- August 16th 2010, 03:10 AMHallsofIvy
Try going to polar coordinates. With and , so that , . Now, just take some upper bound on (it certainly can't be larger than 2) and you have reduced to a one-variable, r, problem.

- August 16th 2010, 03:16 AMthorin
Hi,

So

now, we can use the fact that x.ln(x) has 0 for limit in 0 :

with

- August 16th 2010, 03:49 AMVlasev
HallsOfIvy, please refer to my post in http://www.mathhelpforum.com/math-he...es-153726.html to see an example where your method fails. It fails because there are other ways to approach the limit point, not just straight lines. There is no way to reduce the 2 dimensional problem to a 1 dimensional problem unless it has circular symmetry around the point.

- August 16th 2010, 05:11 AMusagi_killer
- August 16th 2010, 05:20 AMVlasev
- August 16th 2010, 05:21 AMusagi_killer
Oh right, thanks, I get it now!