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06-13-2012, 11:11 AM   #3061
Carpal \'Tunnel

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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by DeucesAx yeah, that's what I meant. So there is no tangent line then? I mean I can't even evaluate the limit, right?

There is a tangent line; it's just vertical. It's of the form x=a. [So here, it's x=e.]

See the graph at:
http://www.wolframalpha.com/input/?i=x*ln%28x%29%2Be^y-xy%3De

Quote:
 Originally Posted by acehole60 When you guys talk about "Rudin" is it "Principles of Mathematical Analysis" (1976)?
That is "Baby Rudin."

"Rudin" is titled "Real and Complex Analysis."

Mariogs is going thru baby Rudin atm, and "Rudin" is a hardcore intro graduate level analysis text.

Quote:
 Originally Posted by acehole60 My plan is to revisit Real Analysis and then Measure Theory. Seems like Rudin is your go-to guy, so I might try him (and will probably also ask questions in this thread). Are there any recommendations for a measure theory book?
Rudin "Real and Complex Analysis"
and
Folland "Real Analysis: Modern Techniques and their Applications"

I think are two of the major ones being used in graduate courses in the big research schools. I learned from Folland and found it fine, but with many annoying typos. I always carried my copy of Rudin as a supplement.

There are a number of other books suggested here: http://mathoverflow.net/questions/11...re-theory-book

But I can't comment further on any of them.

06-13-2012, 05:31 PM   #3062
old hand

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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Wyman "Rudin" is titled "Real and Complex Analysis." Mariogs is going thru baby Rudin atm, and "Rudin" is a hardcore intro graduate level analysis text. Rudin "Real and Complex Analysis" and Folland "Real Analysis: Modern Techniques and their Applications" I think are two of the major ones being used in graduate courses in the big research schools. I learned from Folland and found it fine, but with many annoying typos. I always carried my copy of Rudin as a supplement. There are a number of other books suggested here: http://mathoverflow.net/questions/11...re-theory-book But I can't comment further on any of them.
Thanks a lot. I have done a (undergraduate) course in real analysis before, but I probably need to refreshed it, so I guess I should start with baby Rudin? And then move on to Rudin or possibly straight to measure theory. There seems to be no particular consensus on a measure theory book, so I might just pick one from the list.

Thanks again! I will probably return with questions to exercises.

EDIT: Or do you think I could jump straight into Rudin?

 06-13-2012, 05:52 PM #3063 Carpal \'Tunnel     Join Date: Mar 2007 Location: Redoubling with gusto Posts: 10,706 Re: The Official Math/Physics/Whatever Homework questions thread Measure theory is what a real analysis course (graduate) is all about. So Rudin and Folland contain all you'll ever want to know about it. Or in my case, way more than I could ever want to know...
 06-16-2012, 02:31 PM #3064 adept     Join Date: May 2008 Location: increasing potential GDP Posts: 1,170 Re: The Official Math/Physics/Whatever Homework questions thread We've just learned derivatives of inverse trig functions, and I'm working on a take home quiz. Don't worry, the professor says we can seek help from other people with take home quizzes. Really! Anyway, the structure of this question really confuses me. Could someone please clarify? Find y'(x) if arcsin(xy) = 1 -y*x^2The part that really confuses me is "arcsin(xy)". The question would make a lot more sense to me if it said "arcsin(y(x))", because then I can easily apply the chain rule: $\(arcsin(g(x)))' = \frac{1}{\sqrt{1 - (g(x))^2}}g'(x)$ Do I need to solve "arcsin(xy) = 1 -y*x^2" for y first or am I overthinking it? I really believe the question is not meant to be that complicated for us yet. I suspect that I should just be plugging in "1 -y*x^2" as g(x) in my above formula, but the question just doesn't make sense to me like that. Thank you.
 06-16-2012, 02:34 PM #3065 Carpal \'Tunnel     Join Date: Sep 2005 Location: Berkeley Posts: 13,703 Re: The Official Math/Physics/Whatever Homework questions thread Implicit differentiation.
06-16-2012, 03:47 PM   #3066

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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by Cueballmania Implicit differentiation.

Again:
Find y'(x) if arcsin(xy) = 1 -y*x^2
Just for completeness, note that I'm using this chain rule:
$\(\arcsin(g(x)))' = \frac{g'(x)}{\sqrt{1 - (g(x))^2}}$
This quotient rule:
$\(\frac{g(x)}{f(x)})' = \frac{g'(x)f(x) - g(x)f'(x)}{(f(x))^2}}$
And this product rule:
$\(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)$

My final answer is pretty long, so I'm going to show all my steps. Here we go:

$\(\arcsin(xy))' = (1-x^2y)'$

$\frac{(xy)'}{\sqrt{1-(xy)^2}} = 0-(2xy+x^2y')$

$\rm -}\frac{y+xy'}{\sqrt{1-(xy)^2}} = 2xy+x^2y'$

$\frac{-y}{\sqrt{1-(xy)^2}}-2xy = x^2y'+\frac{xy'}{\sqrt{1-(xy)^2}}$

$\frac{-y}{\sqrt{1-(xy)^2}}-2xy = y'(x^2+\frac{x}{\sqrt{1-(xy)^2}})$

$\rm y' = }\frac{\frac{-y}{\sqrt{1-(xy)^2}}-2xy}{x^2-\frac{x}{\sqrt{1-(xy)^2}}}$

$\rm y' = }\frac{\frac{y}{\sqrt{1-(xy)^2}}+2xy}{\frac{x}{\sqrt{1-(xy)^2}}-x^2}$

Wow. The answer is pretty long, which is still worrisome. Also, I still need to replace y in the derivative by solving the original equation for y:

$\arcsin(xy) = 1 -yx^2$

$\rm y = }\frac{1 - \arcsin(xy)}{x^2}$

I'll just leave it here for now. So far, so good?

 06-16-2012, 04:45 PM #3067 veteran     Join Date: Aug 2009 Location: Stanford, CA USA Posts: 3,322 Re: The Official Math/Physics/Whatever Homework questions thread You can also take the sine of both sides in defining equation meaning ; xy=sin(1-y*x^2) and then take the derivative of both sides and solve for y' which is a lot easier as it requires much simpler derivatives. You still end up with y' as function of x,y. Ps: Dont forget a derivative symbol missing in your last expression y'=...
06-16-2012, 05:00 PM   #3068

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Re: The Official Math/Physics/Whatever Homework questions thread

Wow! Thank you, masque de Z! That makes it much simpler. I need a lot more practice approaching these questions as simply as possible.

I don't see what you're referring to here though:

Quote:
 Originally Posted by masque de Z Ps: Dont forget a derivative symbol missing in your last expression y'=...

06-16-2012, 07:18 PM   #3069
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by non-self-weighter Wow! Thank you, masque de Z! That makes it much simpler. I need a lot more practice approaching these questions as simply as possible. I don't see what you're referring to here though:
Its ok i thought that was the final result for y' but its ok you didnt write anything wrong. I thought something else that is now fine after looking back what you wrote.

 06-16-2012, 11:33 PM #3070 grinder     Join Date: May 2012 Posts: 596 I also have a homework question. I am supposed to find the limit of x^ sin(x) as x approaches 0 from the right. I know I have to write it as y = x^ sin (x) and then take the natural logarithm of both sides to get ln(y) = ln x^ sin (x) which should equal sin (x) * ln(x). But when I apply l' hopitals rule I get stuck. Whatever I put in the numerator it just gets worse with no answer. I googled it, but only found solutions using taylor, we didn't do that yet.
06-17-2012, 07:01 AM   #3071
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by DeucesAx I also have a homework question. I am supposed to find the limit of x^ sin(x) as x approaches 0 from the right. I know I have to write it as y = x^ sin (x) and then take the natural logarithm of both sides to get ln(y) = ln x^ sin (x) which should equal sin (x) * ln(x). But when I apply l' hopitals rule I get stuck. Whatever I put in the numerator it just gets worse with no answer. I googled it, but only found solutions using taylor, we didn't do that yet.
Rewrite sin(x)*Log(x) as sin(x)/(1/Log(x)) and apply L'Hopital rule there.

Then apply it one more time to the resulting expression because you will need the limit of x*(Log(x))^2 which of course you can write as (Log(x))^2/(1/x) and eventually you get x*Log(x) for which you can rewrite as Log(x)/(1/x) and apply L"Hopital again which finally will get you the answer.

Just keep trying never give up and victory is yours , lol. Remembers Churchill lol!

"This is the lesson: never give in, never give in, never, never, never, never—in nothing, great or small, large or petty—never give in except to convictions of honour and good sense. Never yield to force; never yield to the apparently overwhelming might of the enemy"

Seemed appropriate here given that you had to keep using the method over and over again lol.

Probably some easier alternative may exist. The fact is to any experienced approximations guy the original expression is instantly x^x in the limit and you know this is 1 basically from the x(log x) thing that goes to 0 because |log x| doesnt go to infinity as fast as say x^(-1/2) or whatever like that power smaller than 1 making the absolute value of product say between x and x^1/2 both being 0 hence the exponential of 0 =1 for the original thing )

Try to find Sin(x)^(tan(x)) if you want to practice and convince yourself you can do such things anyway without help.

PS: You can even try the original as Log(x)/(1/Sin(x)) and same methods, probably easier Churchill boost free lol...(the log gets killed instantly and you know sin x goes like x etc)

Last edited by masque de Z; 06-17-2012 at 07:14 AM.

 06-18-2012, 01:35 AM #3072 Pooh-Bah     Join Date: Sep 2010 Location: California Posts: 3,624 Re: The Official Math/Physics/Whatever Homework questions thread Hello everyone, I don't know where to ask, and this thread seems like my best bet, but in about a week, I'm going to start learning an introduction financial course to accounting, and I'm trying to look for the best position to ready the mind so that when I start the class, I don't get behind the eight ball right away. So where do I begin for preparation? Also, I might ask questions in the future about accounting if that is all right with you guys.
 06-18-2012, 01:53 AM #3073 grinder     Join Date: May 2012 Posts: 596 The most important question you should ask is: should I make accounting my career? The answer is NO. Accounting sucks. Its ok while you are at college, once you get to a higher level and get to discuss it at a conceptual level. Once you are working it's so dry that you literally wanted to shot myself. I worked for pwc and thus with accountants from multiple companies. They were pretty much all miserable ppl. Sure you'll make good money and have all kinds of career oppurtunities, but you'll have your butt of in a job that sucks. Don't do it. seriously.
06-18-2012, 07:19 AM   #3074
Carpal \'Tunnel

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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
 Originally Posted by DeucesAx The most important question you should ask is: should I make accounting my career? The answer is NO. Accounting sucks. Its ok while you are at college, once you get to a higher level and get to discuss it at a conceptual level. Once you are working it's so dry that you literally wanted to shot myself. I worked for pwc and thus with accountants from multiple companies. They were pretty much all miserable ppl. Sure you'll make good money and have all kinds of career oppurtunities, but you'll have your butt of in a job that sucks. Don't do it. seriously.
They were miserable because they worked at pwc and made 50-60k and worked 90-100 hrs a week. They were not miserable just because of accounting.

The big firms are soul crushing, but I have plenty of accountant friends that work at smaller places (e.g., hedge funds, big companies that hire in-house accountants, etc) who love life. Some of them did 3-4 years at a big firm before that, but most of them used that as an opportunity to sock away money, live in a big city, and bang a lot of accountant girls.

Sorry to disagree so wildly, but I don't think your advice is general at all.

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