Do you have other issues occupying your mind?

i don't really know, but i just can't concentrate on anything right now.

for the moment i have sort of stopped caring about getting my assignments done

i'll help!

give me a homework problem....

There's nothing bothering you more than usual? Nothing you want to talk about? Maybe through PM if not here? Or not at all?

The same thing happens to me every once in a while. In my experience the best way to fix it is to get out of the house for a while and clear your head. Even just going to the store usually helps.

Although using pseud as a calculator works too

sorry pseud, i don't think that that'll do me much good at the moment, i just can't figure out anything from any of my subjects, i must be preoccupied with something, but i just can't figure out what is gnawing at me right now.

im just feeling really down today, nothing bad has happened, but all my thoughts are like clouded over and concentrating is something of a wonder.

well, sorry you are feeling so down. The offer still stands. I won't just do the homework for you either--I'll provide detailed explanations. I'm that bored...

i would type out some of these math problems here, but i literally can not type out the symbols in the problems, but its good old limits with some funny greek letters or something in it.

You can always substitute different letters.... you can just describe what the symbols look like. I'll figure it out...

ok its given as lim x->2 (3x+2)

and another problem of lim x->2 (x^2 - 3)

directions:

find limit L. then find "upside down g symbol" > 0 such that |f(x) - L| < 0.01 whenever 0 < |x-c| < "upside down g symbol"

i can find the limit, but that's all i can do

upside down g = delta...

working on it. (might get interrupted soon--still at work...)

I'm assuming f(x) = 3x+2

f(x) = x^2-3, yeah?

yes, both separate problems too

what's going on with the "c"?

Looks like you're basically finding how small a range you have to confine x to so that f(x) stays within .01 of the limit.

is c supposed to be 2?

yeah, i think

Yeah, yeah--c is 2, the thing x was approaching.

Ok, so the first one goes something like this:

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

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

So you 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:

-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

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 yeilded different numbers, you'd take the smaller one.)

Does that make sense?

Sorry I was gone for a while. Inf, why are you feeling so down today? Is it just the stress of everything adding up?

(Hey pseud)

sorry pseud, you totally lost me yeah, im just that far gone today

hey mm i don't really know, could be i suppose

lim x->2 of f(x) = x^2 - 3 = 1

so |f(x) - L| = |x^2 - 3 - 1| = |x^2 - 4|

|x^2 - 4|<0.01 => -0.01< x^2 - 4 < 0.01

you need to solve for x. Add 4 all the way through:

3.99

sqrt all the way through, but note that x could be negative:

sqrt(3.99)< x < sqrt(4.01) or -sqrt(3.99)>x>-sqrt(4.01). I don't think the negative solutions actually matter.

now for |x-2| < delta, we need sqrt(3.99) - 2 < x - 2 < sqrt(4.01) - 2

which is something like -.00250.... < x-2 < .002498......

so you want to pick delta to be the smaller (in absolute value) of these. And you probably want an exact number, so leave it as delta = sqrt(4.01) - 2. Though any delta smaller than this also works...

Again, basically these questions are asking you how small you have to squish the x range down so that the f(x) stays within .01 of the limit as x approaches 2.

hold on--I'll break it down in smaller steps for you. I realize that looks like a mess (I was trying to figure out what I was doing...).

give me a few minutes...

hey mm i don't really know, could be i suppose

Would talking help, or do you just want to leave it alone and let it pass?

i don't know mm, right now i really just feel like curling up in a ball and laying down, but that is not going to happen anytime soon

I'm sorry you're feeling that way

Would a teddy bear help?

mr. fluffnugget? i think that was his name?