i see all of this new material that i have never seen before it was supposed to be a review, but i don't remember any of this stuff from last year, all we did was finding limits, we never dealt with epsilon or delta or any of that inequality stuff

ok, so you're good with limits, but the whole rest of it threw you...

lets see...

have you solved absolute value inequalities before? Would you know how to take care of something like:

|2x - 1| < 7

or does that look foreign to you?

How comfortable are you with function notation and domains and ranges and all that? Is that pretty new or are you ok with seeing f(x)'s and knowing how to think in those terms fluidly? Did my little conceptual diagram make any sense? Has your teacher ever drawn anything similar?

-3

domains and ranges, done. how to use f(x) easy.

couldnt' take anything out of the diagram and i don't think i've seen anything smilar.

ok. so I think the real issue is that you are having a difficult time interpreting what the problem is asking. You've got all of the tools to work out the mechanics.

conceptually, what is going on:

think about lim x->2 f(x).... It's just a number on the number line, right? In fact, it was 8 in that first problem. So think of 8 sitting on the number line. Now think of all the numbers near 8. In fact, think of all the ones that are within 0.01 of 8. So you've got an interval (7.99, 8.01). (you're familiar with interval notation? just think about all the numbers between 7.99 and 8.01)

Now, f(x) takes numbers from the domain(which happens to be all reals in this case) and maps them to the range (curiously, also all reals in the first example). So f(x) takes numbers and assigns them to different values. Some of those values lie between 7.99 and 8.01. The question is asking, what stuff in the domain gets mapped to that interval between 7.99 and 8.01?

You know that 2 got mapped to 8 (f(2) = 8). And stuff near 2 is going to get mapped to stuff near 8. So how how big can you make an interval around 2 on the numberline and still have everything in that interval get mapped inside the interval between 7.99 and 8.01?

Are you following so far?

sorry pseud, i can't really follow along with text. its not really any use. i'll just have to try to get some help tomorrow. it has kind of gotten me a bit pi$$ed off right now, so im not really sure if i should even be here right now.

So let me try and break this down again:

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

Ok, so we want to look at stuff near L. We want to look at stuff that is within a distance of 0.01 of L on the number line. (This distance of 0.01 .)

We want to know what x can be so that f(x) is within a distance delta of L on the number line.

Now: |f(x) - L| is the mathematical way of expressing the statement “the distance between f(x) and L”. We want this distance to be less than 0.01.

So: |f(x) – L| simply equals |f(x) – 8| (because L = 8) which, if we plug in f(x) equals = |3x + 2 - 8|, which simplifies to = |3x – 6| => |f(x) – L| = |3x – 6|

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

|3x - 6| < 0.01 (note that this the same statement as |f(x) – L| < 0.01 is, just with the relevant function and values plugged in)

So first you solve this inequality to get the values of x which will the function will map inside the interval from 7.99 to 8.01. Are you with me?

sorry pseud, i can't really follow along with text. its not really any use. i'll just have to try to get some help tomorrow. it has kind of gotten me a bit pi$$ed off right now, so im not really sure if i should even be here right now.

agh! seriously. draw diagrams. it helps.

where are you getting lost? I promise, if you can get this one, the rest of it is going to be easy.

the problem is that i literally can not understand a word of what it is asking me, and nothing that has been said is really helping that besides, can't dwell too much on this math, i have other subjects due tomorrow too

The rest of it, anyway....

After solving the inequality, you get 1.99666666666…< x < 2.003333333…

(so the stuff in the domain of the function that lies between 1.996666… and 2.0033333…. gets mapped to the stuff in the range of the function that lies between 7.99 and 8.01)

Now, the last part is just asking what the size of this interval is. Delta is simply the distance between 2 and the ends of this interval.

So 0 < |x – c| < delta => c is just 2, so this becomes 0 < |x-2| < delta, solve for delta. Now, we already know that 1.99666666666…< x < 2.003333333…, so

1.99666666666… - 2 < x – 2 < 2.003333333… - 2

Which becomes

-.00333333…. < x-2 < .00333333…

So delta must be .0033333…

the problem is that i literally can not understand a word of what it is asking me, and nothing that has been said is really helping that besides, can't dwell too much on this math, i have other subjects due tomorrow too

You're making this difficult. You say you don't understand a word of it, but that isn't true. You know what the limit is and you know what to do with inequalities. You're going to have to tell me, as you are reading through what I wrote, at which point is it that there is a sentence that doesn't make sense.

Now I'm wondering if you're maybe missing a conceptual understanding of what fucntions actually do...

This is a pitfall I see with the way math is taught sometimes. You can go through the motions and do the problems because you have learned the algorithms to implement, but if you don't know what's actually going on, it's really hard to advance from there.

I know you have other work to do, an I honestly need to be getting stuff done right now too, but can you tell me what you know about fuctions? What to they do? what is the domain and the range? what does that all mean? Because if those concepts are clear, i don't know how the rest of this isn't following easily from that.

I have an idea...I'm totally going to make you a cartoon about functions....it might be awhile...brace yourself....

in my math, they don't teach why, only how so i can show you how to get all of those, but anything else, no.

ack! that's awful. Knowing the why makes the how soooooo much easier!

Ok, I've got me a project....you WILL learn this stuff. But I'm going to step back and come in slow. Starting with all the conceptual stuff with functions. We'll build the foundation and the rest will follow from there... but I've got a shit ton of crap to get done in before I'm off work, so it might be later tonight....

ya know what, i think that im done with my hw for the night.

i do have a bit left, but i can always do that tomorrow

Hey inf, have you tried http://www.khanacademy.org/? The guy is really good at explaining it, and you have a visual the entire time.

So how are you today?

good i guess mm,

i just remembred khan once you mentioned it, so now im watching anything relating to limits

what is this blasphemy! Am I to be made useless by this so called "khan academy?"

Dude--I highly recommend relearning about functions first. If you don't have a strong intuitive sense for what they are and how they work, you're building on a shaky foundation.

Pseud, Khan Academy trumps all. Enough said .

Inf, let me know what you think of him. He's really helped me in the past.

Also, not to draw attention away from this blog, but I posted one of my own . I've actually got a lot of work to do, so it's probably best I'm not diverted anyway.

Well i suppose I suck far more at explaining math than I ever could have dreamed. I tried.

na pseud, you don't suck, its just that i need to actually see it worked out to know what i am actualy looking at, im a very visual learner and text and a few pictures just can't help me that much, i need either to see someone do it and follow along or in this case, most of the time videos work as well because i can follow along.

Pseud, if it's any consolation, NO ONE would be able to explain any of that stuff to me

kids these days....

don't blame the kid, blame the curriculum lol

ohhhh, careful there. While I agree that good teachers and good curriculum go a long way, the onus is always ultimately on the learner and not the teacher. If you want to learn something, it's up to you to learn it. Sitting back and passively hoping knowledge makes it into your brain is what's wrong with a vast majority of the population. You've got to want to figure it out and struggle to get there. You'll learn it that much better in the end if you own it.