the question and where i got stuck in this link:

http://img187.imageshack.us/img187/8868/44429492ix7.gif

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- Jan 6th 2009, 09:31 AMtransgalacticlimit prooving question..
the question and where i got stuck in this link:

http://img187.imageshack.us/img187/8868/44429492ix7.gif - Jan 6th 2009, 10:45 AMKrizalid
We have to prove the following statement:

$\displaystyle \left| x-5 \right|<\delta \implies \left| x^{2}-25 \right|<\epsilon .$

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Observe that $\displaystyle \left| x^{2}-25 \right|=\left| x+5 \right|\left| x-5 \right|.$ Now pick $\displaystyle \delta=1,$ and $\displaystyle \left| x+5 \right|\left| x-5 \right|\le 11\left| x-5 \right|<\epsilon .$

Hence, conditions are fulfilled if you take $\displaystyle \delta =\min \left\{ 1,\frac{\epsilon }{11} \right\}.\quad\blacksquare$ - Jan 6th 2009, 11:43 AMtransgalactic
my question i about how to choose the value for M

?? - Jan 6th 2009, 11:59 AMtransgalactic
i understand that our upper bound is 11

so inorder for this to work (like your previous examples in the article you published

we need only

$\displaystyle

$$\displaystyle \delta = \frac{\epsilon }{11}

$

why to use minimum??

the previoss werenot solved like that

$\displaystyle

$$\displaystyle \delta =\min \left\{ 1,\frac{\epsilon }{11} \right\}.\quad\blacksquare

$ - Jan 6th 2009, 12:18 PMtransgalactic
we get x as close as possible to 5

|x-5|<1 ==>> -1<x-5<1 so x+5<11

so M>=11

lambda=e/11

why minimum with 1 ?? - Jan 6th 2009, 02:17 PMKrizalid
It's just any number you want.

I took $\displaystyle x\in(4,6)$ because $\displaystyle \delta=1$ is a nice guy. You could've taken other delta, a ratio, 2, whatever. - Jan 6th 2009, 08:20 PMtransgalactic
why you didnt do this min function in the previous examples

in the article? - Jan 6th 2009, 09:11 PMtransgalactic
usually ou ended this question by saying lambda=e/11

why lambda=min{1,e/11}

why 1? why any number i want?

why minimum? - Jan 7th 2009, 12:19 AMtransgalactic
did i prove it correctly

i solved it differently from the article

is that ok?

http://img224.imageshack.us/img224/9929/93418507so5.gif