Nah, this is a new one. Mrfluffnugget (or something like that) is hidden away safely in my Teddy Bear blog.

i may be sleeping with my stuffed animals tonight

The problem asks you to find delta > 0 such that |f(x) - L| < 0.01 whenever 0 < |x-c| < delta.

What is this saying? Let’s go over this conceptually:

Your function f(x) takes numbers from a domain and maps them to a range. So think of D as the domain—in this case it’s the set of all real numbers. And let R be the range (all possible outputs of the function).

Consider what f(2) is in range-land. (These problems are simple enough that lim x->2 of f(x) actually just equals f(2)). Imagine the range, R, as a blob and f(2) as a dot in that blob. Now you’re drawing a circle around f(2) with radius .01. So we’re looking at a small region in the range surrounding f(2). The question is asking, if we go back to the domain and look at all of the values that f(x) maps into this small circle around f(2), how small of a circle to those x values lie in?

I made a picture for you:

i may be sleeping with my stuffed animals tonight

I thought you did that anyway

I was really surprised how much it can help. After I posted that blog a while back, I started hugging an extra pillow when I went to sleep each night . I did that for a while, and it's really only just very recently that I don't really need it to calm me down. Still, I do sometimes find that I still use it

thanks pseud, i may look back at that post tomorrow, since the HW isn't due until um...... 2 days from now.

Now here's how I originally answered it, with a few more comments to try and explain better:

You know already that lim x->2 of f(x) = 3x+2 = 8 = L

so |f(x) - L| = |3x + 2 - 8| = |3x - 6|

So you first need to find out what x has to be to satisfy:

|3x - 6| < 0.01

the absolute value is less than 0.01 as long as what's inside the absolute value bars lies between -0.01 and 0.01. So you can figure out what x can be by solving the following (note that this will give you the set of x values that lie inside the circle or x values that get mapped within 0.01 of f(2)):

-0.01<3x-6<0.01

add 6 all the way through, then divide by 3 all the way through:

5.99/3 < x <6.01/3

So as long as x lies between those two values, then f(x) will be within 0.01 of f(2).

The reason for the x-c (which is really x – 2 in this case) is that it will give us the size of the range. So instead of saying that the x values lie between 5.99/3 and 6.01/3, we will instead be able to say that the x values lie within a certain radius of x = 2 (this will be our delta).

x-c = x-2 so 5.99/3 - 2 < x - 2 < 6.01/3 -2

hence 0< |x -c| < delta-------> the delta is in this case .00333333333333..... (because that's what 6.01/3 - 2 is and what |5.99/3 - 2| is. Note that if those two yielded different numbers, you'd take the smaller one.)

Does that make sense?

thanks pseud, i may look back at that post tomorrow, since the HW isn't due until um...... 2 days from now.

I tried. It's possible I will only confuse you more . I have no idea what parts you were getting stumped on or how comfortable you are with function notation yet or whatever else, so feel free to ask questions when you get to it.

um, not meaning to draw a crowd here, but um... i read through that and got down to the paragraph that started with "so long as x..." and then i started crying, i think im done for tonight

thanks pseud, ill come back and try again tomorrow.

is it that it's overwhelming? or did you get lost? The thing with stuff like this is both remembering all the steps and understanding what they mean and why you are doing them. It looks like a lot, but once you get the big picture in your head, all the little pieces fall into place. I feel like I wish I had a chalk board and you could see...I know I could explain it better. I know you can understand it too. But if you can't focus, taking a step away for a bit is maybe a good idea. When you do come back to it, take it slow and easy and please, don't hesitate to ask me to explain any little part of it further. I'll do the best I can.

Maybe you need more sleep? That could do it. Maybe go to bed earlier?

I'm sorry. I wish I could make it better

If there's anything I can do to help (short of watching and discussing episodes of Spongebob,) I can give it a go...

Yeah, I feel like I'm puking math at you and that probably isn't helpful....

I just feel like if I could show you that you aren't dumb, then that would be a good thing...

but maybe now's not the time.

anything you want to talk about?

not really sure, i am just hoping that all of this stress that im feeling doesn't put me in a hair-trigger state

you know, sometimes something as simple as making a schedule can help--if I have too many things to do, if I can at least see on paper that there are time slots set aside for all of them to get done, i feel a little better. That said, I'm going to go wiht my sleep theory...school just started, yeah? And you've been having to get up disturbingly early. It's monday. The whole school week is ahead of you still. Do you think maybe you might just be very tired?

i don't think so, but its always a possibility.

i couldn't find anymore grapes, so i got the next best thing... potatoes

please tell me you cooked them...:eek:

yeah theyre awesome

work day over = i'm heading home. I'll check in when i get there. until then, enjoy your potatos!

thanks pseud, have a nice drive (or walk or whatevah) home cya soonish

How ya holding up?

good i guess,a bit better, but now im going to have a bit of homework to do extra 2morrow

First and foremost comes your well-being

eh, true, ill manage it all i guess

And hey, you're not the only one. I just wasted the last however many hours, and I've got a load of work due Wednesday. I'll get around to it eventually...