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 Posted: Tue, 7th Apr 2009 07:28 Post subject: Fucking l'Hopital's Rule |
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Lim as x-> 1 of x/((x^2)-1)
After much number wizardry I transform it into:
(x^2 - x)/(x^3 - x^2 - x + 1)
I do l'Hopital's rule and get Does not exist or 1/2. I don't remember how to use the goddamn rule but I suspect the true answer is DNE. But that's besides the point. The girl who asked me how to find the limit said she hasn't learned l'Hopital's rule yet. So how would you do "Lim as x-> 1 of x/((x^2)-1)" without L'Hopital's rule? I feel like a fucking retard for not knowing the answer =/ Help would be appreciated. It's been bugging me awhile.
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LeoNatan
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| Posted: Tue, 7th Apr 2009 10:00 Post subject: |
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The rule doesn't even apply to lim(x->1) of x/(x^2-1). Let f(x) = x, g(x) = x^2-1, so indeed lim(x->1) of x^2-1 is 0, but lim(x->1) of x is 1, while the rule requires both to be 0. The rule doesn't help all that much with the second function either (Let f(x) = x^2-x, then f`(x) = 2x-1, for which then lim(x->1) of f`(x) is not 0, as the rule requires).
The rule is usually useful for calculating undefined limit problems of 0*∞ or 1^∞.
That said, lim(x->1) of x/(x^2-1) is +/-∞. Approaching from the left, it is -∞ and approaching from the right, it is +∞. 
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| Posted: Tue, 7th Apr 2009 10:42 Post subject: |
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why would the rule require f'(x) to be zero in the lim(x->1) ?
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LeoNatan
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| Posted: Tue, 7th Apr 2009 11:09 Post subject: |
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One pass of the rule is not enough to solve the problem of the second function T4E posted.
f(x)=x^2-x
g(x)=x^3-x^2-x+1
lim(x->1) of f(x) = lim(x->1) of g(x) = 0. So far so good, we apply the rule for the first time:
lim(x->1) of f(x)/g(x) = lim(x->1) of f`(x)/g`(x) = lim(x->1) of (2x-1)/(3x^2-2x-1).
Now the problem is lim(x->1) of (2x-1)/(3x^2-2x-1). This problem cannot be solved using the rule this time, because lim(x->1) of 2x-1 (our original f`(x)) is not 0, as the rule requires. So we are stuck with a very similar problem as the original.
The graph after one pass of the rule:
As you can see, it has the same limit at x=1 as the original.
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| Posted: Tue, 7th Apr 2009 11:26 Post subject: |
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For some reason I thought you ment f´(x) should generally be zero which didn't make any sense.
Which program do you use to make the graphs?
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LeoNatan
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| Posted: Tue, 7th Apr 2009 11:30 Post subject: |
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HubU
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| Posted: Tue, 7th Apr 2009 12:31 Post subject: |
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I remember why I hate math
"Music washes away from the soul the dust of everyday life." ~Berthold Auerbach
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LeoNatan
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| Posted: Tue, 7th Apr 2009 12:40 Post subject: |
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This is really basic stuff... 
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| Posted: Tue, 7th Apr 2009 14:20 Post subject: |
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Yep, this is the stuff that ruined my first semester...
Gotta do that whole class again in the third...
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LeoNatan
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| Posted: Tue, 7th Apr 2009 14:46 Post subject: |
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To me the hardest math was harmonic analysis (Fourier transformations, etc) and differential equations. Got only 88 on that god awful test.  For some reason, some old guys think all this shit is necessary for software engineering. 
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| Posted: Tue, 7th Apr 2009 15:06 Post subject: |
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Yep, still have to see the connection between that kinda math and computer science, but whatever...
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LeoNatan
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| Posted: Tue, 7th Apr 2009 15:24 Post subject: |
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Well, to be honest, there is some use for some of the more advanced mathematical stuff in signal processing, computer graphics, etc., but these are specialized paths withing the software engineering area, and while I might be into computer graphics, I have no intentions of getting myself into something like signal processing, so mandating everyone to study these subjects is unreasonable in my opinion.
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WaldoJ
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| Posted: Tue, 7th Apr 2009 15:39 Post subject: |
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STANDARD NERDS!!
| Sin317 wrote: | | I win, you lose. Or Go fuck yourself. |
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| Posted: Tue, 7th Apr 2009 16:10 Post subject: |
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| Posted: Tue, 7th Apr 2009 17:30 Post subject: |
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I totaly loathed fluid mechanics to behonest, but I had to do it due to the line of work I was in, regarding fluids/oils pressure differentials within the chemical and oilrig industry. (alarm devices/fluid controls)..
I hope I never have to bother with another constant component/differential/specific gravity type of calculation ever again.. Its not hard but god so boring after 6 years of it..
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| Posted: Tue, 7th Apr 2009 17:40 Post subject: |
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| iNatan wrote: | | Well, to be honest, there is some use for some of the more advanced mathematical stuff in signal processing, computer graphics, etc., but these are specialized paths withing the software engineering area, and while I might be into computer graphics, I have no intentions of getting myself into something like signal processing, so mandating everyone to study these subjects is unreasonable in my opinion. |
I read your post and immediately thought -> software signal processing! Our professor told us that when we were learning Fouriers transformat. If you want nasty then you need calculus of residues and complex integration. I'm currently studying for exam in mathematical methods in physics and your everyday ordinary differential equations seems like a piece of cake (and even partially dif. eq. aren't that hard, you just need to solve boundary issues).
And Tainted install Mathematica7 it's powerful program for all sorts of math stuff: deriving, integrating, graphs, linear and non-linear transformation... you name it!
Oh yeah and L'Hospital rule applies when your limit is either 0/0 or inf/inf, and since your is 1/0...
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |

Last edited by dingo_d on Tue, 7th Apr 2009 17:44; edited 1 time in total |
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tonizito
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LeoNatan
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| Posted: Tue, 7th Apr 2009 18:05 Post subject: |
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| dingo_d wrote: | | I read your post and immediately thought -> software signal processing! Our professor told us that when we were learning Fouriers transformat. If you want nasty then you need calculus of residues and complex integration. I'm currently studying for exam in mathematical methods in physics and your everyday ordinary differential equations seems like a piece of cake (and even partially dif. eq. aren't that hard, you just need to solve boundary issues). |
What are you studying? Here in Israel education is really not that good, so I could imagine someone in a "proper" Uni studying subjects much more complex, even for software engineering. |
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| Posted: Tue, 7th Apr 2009 18:11 Post subject: |
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| iNatan wrote: |
Here in Israel education is really not that good |
probably because everyone ends up in the military anyway lol
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LeoNatan
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| Posted: Tue, 7th Apr 2009 19:01 Post subject: |
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No, not because of that...
... It's because all the budget goes to the army.  I heard a report that the IDF has $200,000 rockets that can shoot $20-$50 qassam rockets, which fall by the tens daily ahaha.
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| Posted: Tue, 7th Apr 2009 19:36 Post subject: |
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| iNatan wrote: | | dingo_d wrote: | | I read your post and immediately thought -> software signal processing! Our professor told us that when we were learning Fouriers transformat. If you want nasty then you need calculus of residues and complex integration. I'm currently studying for exam in mathematical methods in physics and your everyday ordinary differential equations seems like a piece of cake (and even partially dif. eq. aren't that hard, you just need to solve boundary issues). |
What are you studying? Here in Israel education is really not that good, so I could imagine someone in a "proper" Uni studying subjects much more complex, even for software engineering. |
Physics   It gets interesting as you learn more complex stuff, but it also gets harder by the year. A friend of mine compared it to drugs: you smoke weed and then after you get bored you need something new and interesting like cocaine In the beginning it't fun, but after it gets even funnier
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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LeoNatan
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| Posted: Tue, 7th Apr 2009 21:19 Post subject: |
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Hahaha, well it is very interesting, but never to study in Uni for me. I can sit and read stuff on Wiki all day long (literally), but once I know I will be tested, it's just like my brain shuts down, and nothing goes in, suddenly I drop all interest in the matter.
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| Posted: Tue, 7th Apr 2009 22:37 Post subject: |
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Hey Leo,
thanks a lot for the help buddy. I put it on a graphing calculator this morning and saw what you said
| Quote: | | Hahaha, well it is very interesting, but never to study in Uni for me. I can sit and read stuff on Wiki all day long (literally), but once I know I will be tested, it's just like my brain shuts down, and nothing goes in, suddenly I drop all interest in the matter. |
Yep, same with me. I read random books on my Kindle all day long, but god forbid I get my ass tested on any of it =/ Can't stand textbooks; the only thing I've used me programming textbook so far is a stand to watch movies on from my laptop. And I paid $170 for the damn thing. Fuck my life >.>
| Quote: | | And Tainted install Mathematica7 it's powerful program for all sorts of math stuff: deriving, integrating, graphs, linear and non-linear transformation... you name it! |
Yep, thanks for the tip. All students at our uni get a license of Mathematica for free, so I already got it on my comp I just haven't fired it up yet and learned how to use it. I suppose I'll do that after I finish reading War & Peace (am on final volume today )
Sense Amid Madness, Wit Amidst Folly
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LeoNatan
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| Posted: Tue, 7th Apr 2009 22:39 Post subject: |
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Cheers!
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| Posted: Tue, 7th Apr 2009 22:53 Post subject: |
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If you have any questions about mathematica, I can give you some aid, I had course on uni where we learned how to use math, since we use it in lab. I have tons of .nb files (on Croatian, but I assume you can read it, right ).
Oh I would have been lost without books about physics. We study by Berkley courses and University Physics, which are great books. Feynman has also great books, but I don't have the time to read them all And I would so like to...
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |

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