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anonymous
 one year ago
can someone tell me how to prove for infinite limit with epsilon and delta or N and M?
anonymous
 one year ago
can someone tell me how to prove for infinite limit with epsilon and delta or N and M?

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abb0t
 one year ago
Best ResponseYou've already chosen the best response.0Yes, if you gave us an example, we could.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0l\[\lim_{x \rightarrow \infty}3x^{2}x2/5x^{2}+4x+1\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11\[\lim_{x \rightarrow \infty}~\dfrac{3x^{2}x2}{5x^{2}+4x+1}\] like that ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11so what does it evaluate to ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11you need to know the limit before starting to prove it using epsilondelta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know the limit it's 3/5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but the prove is quite confusing.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11its easy once you know how to play the game

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11Let \(f(x) =\dfrac{3x^{2}x2}{5x^{2}+4x+1} \) given any positive number \(\epsilon\), you have to show that there exists some \(x\) value, after which the difference between \(f(x)\) and \(\dfrac{3}{5}\) is less than \(\epsilon\).

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11Given any positive number \(\epsilon\), prove that there exists some \(x\) value beyond which below is true : \(\left\dfrac{3x^2x2}{5x^2+4x+1}\dfrac{3}{5}\right\lt \epsilon\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11simplify and try expressing \(x\) in terms of \(\epsilon\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0simplify? sorry where is delta?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0Simplify so that you can find the bound on delta. You have to work backwards

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11yeah what we're doing is just scratch work to express \(x\) in terms of \(\epsilon\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\epsilon< equation<\epsilon\] i get this...what is next?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11for \(x\gt 1\), we have : \( \left\dfrac{3x^2x2}{5x^2+4x+1}\dfrac{3}{5}\right\\~\\ =\left\dfrac{17x+13}{5(5x^2+4x+1)}\right\\~\\ \lt\left\dfrac{17x+13}{25x^2}\right\\~\\ \lt\left\dfrac{17x+17x}{25x^2}\right\\~\\ =\left\dfrac{34}{25x}\right\\~\\ \) \(\dfrac{34}{25x} \lt \epsilon \implies x \gt \dfrac{34}{25\epsilon}\) therefore \(x = \dfrac{34}{25\epsilon}\) works, now you can start the proof.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry, how can i relate x and delta... if it x wasn't approaching to infinity i would say /xa/>delta

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11The definition for limits at infinity is slightly different : \(\lim\limits_{x\to\infty}f(x)=L\) means that for "every" \(\epsilon\gt 0\), there exists some \(x\) value, \(N\), such that \(f(x)L\lt\epsilon\) for all \(x\gt N\).

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11In present problem, we have cooked up that \(N\) to be \(\dfrac{34}{25\epsilon}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11you choose "any" positive \(\epsilon\), the value \(f(x)\frac{3}{5}\) will always be less than that chosen \(\epsilon\) whenever \(x\) is greater than \(\dfrac{34}{25\epsilon}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11In other words, we can make \(f(x)\) as close to \(\frac{3}{5}\) as we want by making \(x\) sufficiently large.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.11I think this is same as the N and M definition that you were refering to in main question
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