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anonymous
 one year ago
For the limit
lim
x → 2
(x3 − 4x + 3) = 3
illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.)
anonymous
 one year ago
For the limit lim x → 2 (x3 − 4x + 3) = 3 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know how to do parablas but not cubic

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0I don't remember these so well :) So take what I say with a grain of salt lol When your x is within delta of 2,\[\large\rm 0\ltx2\lt\delta\]Then the distance between your function and the limiting value should be within epsilon,\[\large\rm x^34x+33\lt\epsilon\]So you've gotta do some work on this thing, ya?\[\large\rm x^34x\lt\epsilon\]\[\large\rm x(x^24)\lt\epsilon\]And then maybe apply Difference of Squares, ya? :o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\large\rm x(x2)(x+2)\lt\epsilon\]And then umm... how do we wrap these up? I'm trying to remember haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0umm your guess is better than mine lol. im teaching myself this

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Let's put a restriction on delta, let it be small... say less than or equal to 1.\[\large\rm 0\ltx2\lt\delta\le1\]\[\large\rm x2\lt1\]\[\large\rm 1\lt x2\lt 1\]\[\large\rm 2\lt x\lt 2\]So that ummm... If x is between 2 and 2, the junk in our epsilon equation is between these values,\[\large\rm 0\lex(x+2)\le8\]The larger of those is 8, so we'll use that.\[\large\rm x(x+2)~\cdot~(x2)\lt\epsilon\]\[\large\rm x(x+2)~\cdot~(x2)\lt8~\cdot~(x2)\lt\epsilon\] So then uhhh... we would want the minimum value for this distance (x2). Either \(\large\rm \frac{\epsilon}{8}\) or \(\large\rm \delta\).

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Hopefully I'm doing this right :P Look at that, lemme know if it doesn't make sense..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im confuse I think im going to a math lab thanks for your help

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Woops, when I added the 2 to each side of the inequality it should have given this: \(\large\rm 1\lt x\lt 3\) Which would change things a bit. But ya, go to math lab c: figure some stuff out.
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