Search found 270 matches

by Eastwinn
Sun Nov 28, 2010 11:35 pm UTC
Forum: Mathematics
Topic: A little homework help (mean value theorem)
Replies: 11
Views: 889

Re: A little homework help (mean value theorem)

^ Well, if f and g are both continuous on [a,b], f + g is continuous as well. So in the case of x+1/x, it's a matter of whether x is continuous on [2,3] (yup) and whether 1/x is continuous on [2,3] (yup). I can't imagine them wanting more detail than that.
by Eastwinn
Sun Nov 28, 2010 5:54 pm UTC
Forum: General
Topic: Hifaleetin' thoughts
Replies: 90216
Views: 9223334

Re: Momentary/Meandering/Meditations (Random like the plague

Thesh wrote:Kind of like how cold water boils faster than hot water?


Yeah, it's surprises like that that reserve my judgment.
by Eastwinn
Sun Nov 28, 2010 5:42 pm UTC
Forum: General
Topic: Hifaleetin' thoughts
Replies: 90216
Views: 9223334

Re: Momentary/Meandering/Meditations (Random like the plague

My mom just claimed to me that running a can of frozen soda under cold water would melt it faster than running it under hot water. That seems silly to me, but I don't want to dismiss it automatically. Stranger things do occur in this world.
by Eastwinn
Thu Nov 25, 2010 5:00 pm UTC
Forum: Mathematics
Topic: Closed form expression for an integral
Replies: 5
Views: 725

Re: Closed form expression for an integral

jestingrabbit wrote:Sure about that?


Woops, I misread the original post as [imath]\int e^{{-(x + b)}^2} dx[/imath]
by Eastwinn
Thu Nov 25, 2010 2:33 pm UTC
Forum: Mathematics
Topic: Closed form expression for an integral
Replies: 5
Views: 725

Re: Closed form expression for an integral

Even though you said no series...

[math]\frac{1}{2}\sum_{n=0}^{\infty}\frac{(-1)^{n}(x+b)^{2n+1}}{n!(2n+1)}[/math]

Edit: Fuck, this is wrong.
by Eastwinn
Wed Nov 24, 2010 1:25 am UTC
Forum: Mathematics
Topic: Alternate Definitions of the Gamma Function
Replies: 9
Views: 1155

Re: Alternate Definitions of the Gamma Function

The Bohr-Mollerup Theorem says that there is only one function that satisfies f(x+1) = x f(x), f(1) = 1, and log-convexity, and that function is Gamma. I'm yet to understand the proof, however, but still if I can show that the alternative definition in the OP is log-convex then that will be sufficie...
by Eastwinn
Tue Nov 23, 2010 11:24 pm UTC
Forum: Mathematics
Topic: Alternate Definitions of the Gamma Function
Replies: 9
Views: 1155

Re: Alternate Definitions of the Gamma Function

^ I've been pronouncing it wrong then :oops: Does your text anywhere mention that Gamma is the unique analytic function which satisfies the recurrence formula and \Gamma(1)=1 ? Its true, even if it doesn't prove it, though I suspect it does. Thank for the response. Yes, it does. It names a t...
by Eastwinn
Tue Nov 23, 2010 6:22 pm UTC
Forum: Mathematics
Topic: Alternate Definitions of the Gamma Function
Replies: 9
Views: 1155

Alternate Definitions of the Gamma Function

I was reading Gamma by Julian Havil and I got hung up on one of the alternate definitions it gave for the Gamma function. It then used that definition to derive an extension of Gamma that converges for all C sans negative integers. It says that Euler (hey, BTW, what is the proper way to pronounce hi...
by Eastwinn
Tue Nov 23, 2010 5:42 pm UTC
Forum: Mathematics
Topic: Probably not feasible, but...
Replies: 8
Views: 987

Re: Probably not feasible, but...

But you also don't need to be formally published in an approved math journal to be able to demonstrate your talents and interests. If you read some mathematical book that is outside the high school curriculum and write your own thoughts about it (like reproving some of the fundamental results in yo...
by Eastwinn
Mon Nov 22, 2010 1:52 am UTC
Forum: Mathematics
Topic: Simple Natural Log question
Replies: 3
Views: 519

Re: Simple Natural Log question

Your mistake was in the last line -- you subtracted e^2 from both sides but managed to remove e altogether :P
by Eastwinn
Sun Nov 21, 2010 4:28 am UTC
Forum: Mathematics
Topic: L'Hospital's Rule, or l'Hopital's rule?
Replies: 10
Views: 5540

Re: L'Hospital's Rule, or l'Hopital's rule?

How do you pronounce this anyway? I've heard so many different versions but I figure someone on here speaks French and can give me a correct pronunciation.
by Eastwinn
Sat Nov 20, 2010 3:41 pm UTC
Forum: Mathematics
Topic: Entire Function That Agrees with Log on Natural Numbers?
Replies: 25
Views: 3565

Re: Entire Function That Agrees with Log on Natural Numbers?

I'd suggest log(|x|+1) but it's not everywhere differentiable. But it's close! It has to be C-differentiable and not just R-differentiable to be entire, and this function isn't C-differentiable anywhere. (The absolute value function is not terribly nice from the point of view of complex analysis.) ...
by Eastwinn
Fri Nov 19, 2010 3:05 am UTC
Forum: Mathematics
Topic: Entire Function That Agrees with Log on Natural Numbers?
Replies: 25
Views: 3565

Re: Entire Function That Agrees with Log on Natural Numbers?

I'd suggest log(|x|+1) but it's not everywhere differentiable. But it's close!
by Eastwinn
Wed Nov 17, 2010 3:54 am UTC
Forum: Mathematics
Topic: Tricky limit problem for a calculus course
Replies: 32
Views: 2883

Re: Tricky limit problem for a calculus course

Did anyone bother to prove that the original limit even exists? EDIT: Nevermind, the answer to that is yes.
by Eastwinn
Tue Nov 16, 2010 11:27 pm UTC
Forum: General
Topic: Glass half full/empty?
Replies: 64
Views: 5791

Re: Glass half full/empty?

Are you filling it or emptying it?
by Eastwinn
Tue Nov 09, 2010 10:37 pm UTC
Forum: Mathematics
Topic: Can (PI) exist?
Replies: 24
Views: 4875

Re: Can (PI) exist?

Circles and polygons don't exist in the real world at all!
by Eastwinn
Thu Nov 04, 2010 6:51 pm UTC
Forum: Music
Topic: Screaming in Music
Replies: 34
Views: 7489

Re: Screaming in Music

TheAmazingRando wrote:
traveltheory wrote:Id still say the only bands that made any good use of it were the ones who started the trends ten years ago.
Started the trends? Screamo is 20 years old, early-00s was the second wave.


Screaming might as well be older than screamo. At least, harsh vocals have been around way before screamo.
by Eastwinn
Wed Nov 03, 2010 11:25 pm UTC
Forum: General
Topic: Logical fallacies/douchebaggery in commercials.
Replies: 4973
Views: 751720

Re: Logical fallacies/douchebaggery in commercials.

I also like how they specify an abbreviation for purchase, as though that's going to be an option, at some point. "No, I think I'll just rent this plane ticket, instead." Sounds perfectly reasonable to me. Pay half price at first, and then when you're half way there, pay the rest. Then if...
by Eastwinn
Wed Nov 03, 2010 8:46 pm UTC
Forum: General
Topic: Logical fallacies/douchebaggery in commercials.
Replies: 4973
Views: 751720

Re: Logical fallacies/douchebaggery in commercials.

"A bikini-clad beauty skied into a wall of snow, then recovered in the warmth of a Columbia Omni-Heat jacket." This is the exact text from a facebook ad. I won't buy their jacket because this bikini-clad beauty's skiing skills aren't good enough. Omni -Heat Jacket? I was hoping my warmth ...
by Eastwinn
Wed Nov 03, 2010 3:24 am UTC
Forum: General
Topic: Logical fallacies/douchebaggery in commercials.
Replies: 4973
Views: 751720

Re: Logical fallacies/douchebaggery in commercials.

Shaving system? Fuck, I gotta go out and buy one of those.
by Eastwinn
Mon Nov 01, 2010 2:53 am UTC
Forum: General
Topic: TvTropes.org
Replies: 28
Views: 15759

Re: TvTropes.org

(yes, I know you can't start a sentence with a conjunction). Says who? I like the Didn't Do The Research subtropes, but I don't venture far out of there. I find those to be interesting, like most common-misconception-themed writing, because I feel like I'll learn something that I'll be constantly r...
by Eastwinn
Sat Oct 30, 2010 4:04 pm UTC
Forum: Mathematics
Topic: limit question
Replies: 13
Views: 1588

Re: limit question

keeperofdakeys wrote:Surely it shouldn't be too hard to show them the squeeze theorem, it can be derived straight from the unit circle.


I think that he's trying to use Sinx/x to demonstrate a proof with the epsilon-delta definition using something his students would already be familiar with.
by Eastwinn
Mon Oct 25, 2010 12:35 am UTC
Forum: Mathematics
Topic: Quick Quadratic Question
Replies: 22
Views: 1515

Re: Quick Quadratic Question

Since a quadratic equation with roots \alpha and \beta is (x-\alpha )(x-\beta )=0 , you can also prove the quadratic equation by once again observing this: \alpha = \frac{-b+\sqrt{b^{2}-4ac}}{2a} \; \;, \;\; \beta = \frac{-b-\sqrt{b^{2}-4ac}}{2a} And then substituting the RHS of each...
by Eastwinn
Sun Oct 24, 2010 11:27 pm UTC
Forum: Mathematics
Topic: Disguised forms of 2
Replies: 114
Views: 13102

Re: Disguised forms of 2

[math]\frac{4}{\sqrt{\pi }}(\frac{1}{2})![/math]
by Eastwinn
Sun Oct 24, 2010 3:39 pm UTC
Forum: Science
Topic: How can I become a genius scientist?
Replies: 12
Views: 2522

Re: How can I become a genius scientist?

If you're trying to become more creative, I wouldn't personally recommend an ADHD medication. Those tend to have the opposite effects.
by Eastwinn
Sun Oct 24, 2010 6:36 am UTC
Forum: Mathematics
Topic: Quick Quadratic Question
Replies: 22
Views: 1515

Re: Quick Quadratic Question

Do you know the quadratic formula? If so, separate it into two equations, one where the radical is added and one where it is subtracted. Since the average of the two roots is the x value of the vertex, taking the average of both of those equations, which represent the roots in terms of a, b, and c, ...
by Eastwinn
Sun Oct 24, 2010 12:04 am UTC
Forum: Serious Business
Topic: It is irrational for me to be upset when people buy dogs?
Replies: 104
Views: 13915

Re: It is irrational for me to be upset when people buy dogs

Some people think that dogs in shelters are all unhealthy or disfigured. This could be the case with your friend.
by Eastwinn
Wed Oct 20, 2010 12:35 am UTC
Forum: School
Topic: Hard work vs. Smartishness
Replies: 247
Views: 39014

Re: Hard work vs. Smartishness

I'm a high school student, and have noticed that the people who get the best grades and the people who are the most intelligent aren't the same people. The students who get good grades know how the school system works and how to (exploit? That word seems a little negative) it. They know how to give...
by Eastwinn
Mon Oct 18, 2010 11:34 pm UTC
Forum: School
Topic: Paul Graham on Nerds, Popularity, and thus School
Replies: 48
Views: 9079

Re: Paul Graham on Nerds, Popularity, and thus School

While I'm extremely tempted to agree that highscool is all just a game, could it be that both of our teenage rebellious spirits are speaking?
by Eastwinn
Fri Oct 15, 2010 12:48 am UTC
Forum: Mathematics
Topic: interesting integral proof i just can't solve...
Replies: 5
Views: 1224

Re: interesting integral proof i just can't solve...

Mathematica says that you're correct. I have no insight in proving it though.
by Eastwinn
Mon Oct 11, 2010 2:32 am UTC
Forum: Mathematics
Topic: tan(9x)/x
Replies: 8
Views: 1944

Re: tan(9x)/x

In case you are still having trouble, here's how to solve the sin(9x)/x limit you're having trouble with. It's a neat little trick. \lim_{x \to 0}\frac{sin(9x)}{x} = \lim_{x \to 0}\frac{sin(9x)}{x} \: \cdot \: \frac{9}{9} = \lim_{x \to 0}\frac{9\:\cdot sin(9x)}{9x} = 9\:\cdot...
by Eastwinn
Sun Oct 10, 2010 9:19 pm UTC
Forum: Mathematics
Topic: tan(9x)/x
Replies: 8
Views: 1944

Re: tan(9x)/x

Consider that you don't necessary have to make that equation look like sin(x)/x. You could also try turning it into sin(9x)/9x. Since 9x->0 as x->0, the limit of both as x->0 is the same value, 1.
by Eastwinn
Sun Oct 03, 2010 4:55 am UTC
Forum: General
Topic: REALLY Annoying Misconceptions
Replies: 4059
Views: 371062

Re: REALLY Annoying Misconceptions

I don't like it when people connect Pi to infinity or random chaos. The digits are only infinite and random with an integral base system. If I wrote it in base pi it wouldn't be infinite. If I wrote it as a continued fraction, it wouldn't be random. Ha, Pi is like the opposite of chaos. Hype about ...
by Eastwinn
Sat Oct 02, 2010 4:35 am UTC
Forum: Mathematics
Topic: A math paper.
Replies: 6
Views: 1651

Re: A math paper.

If I were in your situation, that would be my topic of choice. There's a lot to say.
by Eastwinn
Tue Sep 28, 2010 12:44 am UTC
Forum: Mathematics
Topic: Really basic stuff that was never proven in class
Replies: 83
Views: 11206

Re: Really basic stuff that was never proven in class

Google reveals tons of proofs for the harmonic series's divergence. A lot of them are really clever!
by Eastwinn
Mon Sep 27, 2010 7:24 pm UTC
Forum: Mathematics
Topic: Really basic stuff that was never proven in class
Replies: 83
Views: 11206

Re: Really basic stuff that was never proven in class

^ Yeah, I've seen that before. It's not rigorous but I'm sure we'd all agree that it's suitable to show to a 6th grader.

I did have a great math teacher back then. I did visit him one day and I told him how much I appreciated what he taught me.
by Eastwinn
Mon Sep 27, 2010 5:20 pm UTC
Forum: Mathematics
Topic: Really basic stuff that was never proven in class
Replies: 83
Views: 11206

Re: Really basic stuff that was never proven in class

Back in 6th grade my "Honors Math" teacher was a big Number Theory freak. Prime numbers were his favorite topic to discuss with us. He told us that there were infinitely many. Being in 6th grade, none of us questioned him, but thinking back I don't think he ever proved it to us. That's pre...
by Eastwinn
Sun Sep 26, 2010 6:05 pm UTC
Forum: School
Topic: Hard work vs. Smartishness
Replies: 247
Views: 39014

Re: Hard work vs. Smartishness

Intelligence a curse? Oh please.
by Eastwinn
Sun Sep 26, 2010 2:27 am UTC
Forum: General
Topic: The XKCD smiley
Replies: 17
Views: 2883

Re: The XKCD smiley

Whelan wrote:Besides, it's xkcd, not XKCD.


xkcd is just XKCD with permanent damage from a stoke and a side mullet with bed head. Still works. Totally.
by Eastwinn
Sun Sep 26, 2010 2:17 am UTC
Forum: Mathematics
Topic: I want to be better at maths.
Replies: 12
Views: 1853

Re: I want to be better at maths.

This is a big reason why students struggle in Algebra classes: they're taught rules, but no one encourages (or forces) them to study the relationships to understand the deeper meanings behind the shortcuts. In many ways, learning more advanced forms of mathematics requires the same sort of deconstr...

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