Limit help, confused


by CrossFit415
Tags: confused, limit
CrossFit415
CrossFit415 is offline
#1
Sep10-11, 06:06 PM
P: 162
Prove; limit as x->1 (x^3-5x+6) = 2, epsilon=0.2

I got |x^3-5x+6-2|<0.2

Then I don't know where to go from there. Should I add 2 to 0.2 first or subtract 2 from 6 to get x^3-5x+4 < 0.2 ?

I'm on mobile can't use latex. Thanks
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Tomer
Tomer is offline
#2
Sep10-11, 06:13 PM
P: 202
What do you mean by "epsilon = 2"? Are you supposed to find a suitable delta?
CrossFit415
CrossFit415 is offline
#3
Sep10-11, 06:19 PM
P: 162
Whoops I meant 0.2 Yea I'm trying to find delta.

Tomer
Tomer is offline
#4
Sep10-11, 06:30 PM
P: 202

Limit help, confused


Since you somehow want to use the fact that |x-1| < [itex]\delta[/itex], you should be trying to divide this polynomial by x-1.
Then you'll have |x3-5x+4| = |x-1| |P(x) | < [itex]\delta[/itex] |P(x)|, where P(x) is some other polynomial of order 2, which you could also bound...

Try that. :)
CrossFit415
CrossFit415 is offline
#5
Sep10-11, 06:38 PM
P: 162
I'm sorry but I still do not understand. Couldn't we just solve for epsilon then replace it for delta? Thanks
Tomer
Tomer is offline
#6
Sep10-11, 06:50 PM
P: 202
Quote Quote by CrossFit415 View Post
Whoops I meant 0.2 Yea I'm trying to find delta.
Quote Quote by CrossFit415 View Post
I'm sorry but I still do not understand. Couldn't we just solve for epsilon then replace it for delta? Thanks
I don't exactly understand what you mean.

You wrote |x^3-5x+6-2|<0.2
Defining f(x)= x3 - 5x + 6
But it's not that you need to solve an inequality. What you need to do, formally, is to find a [itex]\delta[/itex], so that for every x that holds |x-1| < [itex]\delta[/itex],
|f(x) - 2|| < 0.2.

So, like I said, you have to somehow use the fact that |x-1| < [itex]\delta[/itex].
You start off by writing |x3 - 5x + 6 - 2|, and you start looking for ways to somehow express it with, apart from other things, [itex]\delta[/itex]. You are looking to see how small this [itex]\delta[/itex] needs to be, so that |x3 - 5x + 6 - 2| is small enough.

You start off in the way I wrote. Otherwise - I don't understand your question.
CrossFit415
CrossFit415 is offline
#7
Sep10-11, 07:03 PM
P: 162
Well it asks me use the graph to find a number Delta.

If |x-1| < d then |(x^3-5x+6)-2|<0.2

Then it tells me find Delta that corresponds to epsilon =0.2

Oh ok, Im starting to see it.


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