Large Hardon Collider

[Woozie]

Having some really serious problems with this proof on a practice exam I was given. My professor said something like this will definitely be on the final I have on Thursday, so if anyone has any suggestions they would be very appreciated. Here's the question:

Suppose that (H1) f is defined on (-2,2) and (H2) f is differentiable at 0 and f'(0)=3. Do not assume that f is differentiable anywhere else. Show that there must exist a positive d (d = delta) such that f(x) > f(0) + 2.9 (x-0) whenever 0 < x < d.

I honestly do not really have any clue where to go with this, so I'll edit this post with my work when I actually come up with something. Just wanted to post this now to see if anyone sees something I'm missing.

Just solve for 2.9

http://latex.codecogs.com/gif.latex?...0)}{x-0}%3E2.9

Subtract 3 from each side

http://latex.codecogs.com/gif.latex?...-0}-3%20%3E-.1

The idea is to get an expression you know something about, which we now have (we know about the expression on the left here). We know that if this final statement is true, then the statement which is to be proven is true. We also know that the expression on the left goes to zero, and hence must eventually become bigger than -0.1. In fact, we know that if we make

http://latex.codecogs.com/gif.latex?...3|%20%3C%200.1, then it automatically follows that

http://latex.codecogs.com/gif.latex?...-0}-3%20%3E-.1

and hence f(x) > f(0) + 2.9 (x-0)

And we know we can make the statement http://latex.codecogs.com/gif.latex?...3|%20%3C%200.1 true by choosing a small enough δ1 such that |x-0| < δ1. Choose δ = min{δ1,2} (since your function is only defined in (-2,2). Then your statement is true on 0 < x < δ because it's true on -δ < x < δ and (0,δ) is a subset of (-δ,δ).

[Ferion]

Thank you so much Woozie, I really appreciate the help. I think the way the problem was set up just really threw me off because this was actually a very easy problem.

[Eliseos]

I will never understand mathematicians, that seems like such a silly thing to solve for

[Woozie]

Well, the idea really was to force him to use the definition of the derivative, though that was a weird way to do it.

[Eliseos]

Silly! Also finals week sucks the big one

[Woozie]

Yeah, last week was terrible, wasn't it?

[Eliseos]

If you are implying that your finals were last week and not this week, then I, with respect, hate you

I don't think I've ever been this busy for a finals week. I could handle all the studying for the finals, but the extra work I have to do for all these classes that had mismanaged time is dumb. Woozie write my optical pumping lab report for me please.

[Woozie]

I didn't even write my own lab reports until a month after the semester ended. So unless it's not due until the middle of January, you probably don't want me writing it lol

[Ferion]

Sorry for another math question. I know how to do the proof for this problem, but I'm not exactly sure if I'm exactly answering what is being asked.

Suppose that (H1) f is strictly monotone increasing on [0,2] (H2) A = {f(x): 0 < x <= 2}
(A) Show that lim (x->0) f(x) must exist.
(B) Show that f(0) <= lim (x->0) f(x).

My problem is that I'm not exactly sure I answered what they're asking. For part (A) I basically did a epsilon-delta proof that showed lim(x->0)f(x) is equal to its greatest lower bound. I'm not exactly sure if this is correct now though considering part (B). It feels like I answered both parts in my epsilon-delta proof, but I feel like I'm really missing something. Once again, thank you for any advice.

[Eliseos]

I didn't even write my own lab reports until a month after the semester ended. So unless it's not due until the middle of January, you probably don't want me writing it lol

It feels like I won't finish these lab reports until sometime then, they are so long and unnecessary. If people weren't so sciencedum we wouldn't have to write these things like an idiot is our reader.

[Shiroikage]

That's completely missing the point of scientific writing.

[Eliseos]

Maybe, but my professor isn't going to read anything I send him, so these reports are just a waste of time when I could be studying for my finals.

[Woozie]

Sorry for another math question. I know how to do the proof for this problem, but I'm not exactly sure if I'm exactly answering what is being asked.

Suppose that (H1) f is strictly monotone increasing on [0,2] (H2) A = {f(x): 0 < x <= 2}
(A) Show that lim (x->0) f(x) must exist.
(B) Show that f(0) <= lim (x->0) f(x).

My problem is that I'm not exactly sure I answered what they're asking. For part (A) I basically did a epsilon-delta proof that showed lim(x->0)f(x) is equal to its greatest lower bound. I'm not exactly sure if this is correct now though considering part (B). It feels like I answered both parts in my epsilon-delta proof, but I feel like I'm really missing something. Once again, thank you for any advice.

Edit: I'm an idiot. Let me redo this.

Edit 2: Actually I'll probably get back to this later or tomorrow. I'm a little busy today. If you post your proof I may be able to proof read it sooner than I can write my own.

Edit 3: Actually, don't bother posting your proof. It's definitely wrong. Unless I'm missing something, the infimum/greatest lower bound doesn't have to be the limit. Here's an example of why.

[archibaldcrane]

Hey nerds. I wanna buy my dad a few books about space and stuff for christmas - he's interested in the immensity of the universe, possibility of life, solar systems, planets, the big bang, whatever. He's a retired high school math teacher so some numbers and formulas won't scare him off, but calc level or beyond escapes him. I'm probably going to get him "A Brief History of Time" as a classic, but I'm looking for others in that range. Probably 3 or 4 total, preferably that I can pick up at a Barnes and Noble or the like.

Get at me.

[Tyche]

Took someone's suggestion in this thread and told an in-law to buy me "The Elegant Universe" by Brian Greene for Christmas.

[Eliseos]

Can't go wrong with Brian Greene, Neil deGrasse Tyson, or Richard Feynman. The most complicated math in those (unless you get the Feynman lectures) is algebra, and even then formulas are pretty rare. The Fabric of the Cosmos (Greene), Death by Black Hole and Origins(both by NDT) are all good reads.

[Woozie]

When it comes to space stuff, Miz is probably the best person to ask. My suggestions would probably be geared more towards quantum/particles/high energy stuff (but these books do have a fair amount of space stuff, and lots of big bang stuff).

The Elegant Universe - Brian Greene
Fabric of the - Brian Greene (anything by Greene, really. Same with Hawking. Kaku is an interesting guy, but his books aren't purely space/big bang/etc).
The Universe in a Nutshell - Stephen Hawking.

Every other good book I can think of off the top of my head is almost purely quantum/particle/high energy stuff. Like "The End of Physics", "The Particle Garden", "The God Particle", etc.

You could also try getting him some Carl Sagan DVDs or a subscription to Scientific American or something similar but more space oriented. Miz would know more than I would.

It probably doesn't need to be said, but ignore anything Max says about space. I wouldn't even trust his book suggestions unless someone else says it too.

Edit: Don't forget what NDT did to Pluto. If you buy his book, you may as well be supporting terrorists.

[archibaldcrane]

Pluto should've manned up and cleared it's own orbit if it wanted to play with the big boys.

[Max™]

It probably doesn't need to be said, but ignore anything Max says about space. I wouldn't even trust his book suggestions unless someone else says it too.

http://t2.gstatic.com/images?q=tbn:F...cjlsr.jpeg&t=1

My suggestions would be Six Easy Pieces, and Six Not So Easy Pieces, Feynman rules.

[Mizango]

Hey nerds. I wanna buy my dad a few books about space and stuff for christmas - he's interested in the immensity of the universe, possibility of life, solar systems, planets, the big bang, whatever. He's a retired high school math teacher so some numbers and formulas won't scare him off, but calc level or beyond escapes him. I'm probably going to get him "A Brief History of Time" as a classic, but I'm looking for others in that range. Probably 3 or 4 total, preferably that I can pick up at a Barnes and Noble or the like.

Get at me.

Like has already been suggested, Brian Greene is fantastic. But if you are looking for introductory books and easy reading (Not sure of you fathers knowledge on the subject) then id go with these:

http://www.amazon.com/Origins-Fourte.../dp/0393327582

http://www.amazon.com/Universe-Down-...ef=pd_sim_b_13

http://www.amazon.com/Briefer-Histor...ref=pd_sim_b_4

http://www.amazon.com/Universe-Nutsh...ref=pd_sim_b_2

If he is intrigued by Wormholes, Gravity, QM, Exoplanets etc.. I have suggestions for those too. Check those reviews son, your boy posting dat hot fire. Those are just a few books that wont overwhelm him to the point of irritation. I know we've talked and joked about your dad on FB and he smart, so feel free to ask me for anything else.

Fabric of the Cosmos by Brian Greene is a good one too. If he likes Theoretical physics and possibilities on things like white holes, the multiverse and things related to VSL and alternate theories on inflation then check out works by Smolin, Kaku or João Magueijo.