You are not logged in.
#101 2011-06-30 20:41:05
- bobbym
- Administrator
Online
Re: Limits!
Hi;
I got - ∞ for the one with the z in there. Thanks much for providing your solution.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#102 2011-06-30 20:48:25
- gAr
- Star Member
Offline
Re: Limits!
Hi,
Okay.
You could've figured it out that there could be a mistake.
Thanks for telling!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#103 2011-06-30 22:48:53
- anonimnystefy
- Real Member
Offline
Re: Limits!
hi gAr
could you explain how you got the second line in your solution.i don't get it.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#104 2011-06-30 23:01:08
- gAr
- Star Member
Offline
Re: Limits!
Hi anonimnystefy,
I used L'Hospital's rule.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#105 2011-06-30 23:04:03
- anonimnystefy
- Real Member
Offline
Re: Limits!
aah.ok think i get it.
could you also make a topic on integrals?it would be nice to practice working on them.
Last edited by anonimnystefy (2011-06-30 23:05:20)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#106 2011-06-30 23:12:57
- bobbym
- Administrator
Online
Re: Limits!
Hi;
You can find a lot of them here.
http://www.mathisfunforum.com/viewtopic.php?id=4208
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#107 2011-06-30 23:21:29
- gAr
- Star Member
Offline
Re: Limits!
Hi bobbym,
I was searching for that url. Thanks!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#108 2011-06-30 23:25:59
- bobbym
- Administrator
Online
Re: Limits!
Hi gAr;
I can not come up with anything better for #9 then using L'Hospitals rule.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#109 2011-06-30 23:45:27
- gAr
- Star Member
Offline
Re: Limits!
Okay, no problem.
Thanks for looking into the problem.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#110 2011-06-30 23:48:51
- bobbym
- Administrator
Online
Re: Limits!
Hi;
This works. Taylorize the numerator:
Now divide through by x and now it is easy to see what the limit is.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#111 2011-06-30 23:56:26
- gAr
- Star Member
Offline
Re: Limits!
Hi bobbym,
Yes, I tried expanding like that.
But deriving that would require us to find limits anyway!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#112 2011-06-30 23:59:47
- bobbym
- Administrator
Online
Re: Limits!
Hi;
Do you mean the derivatives, because the limits are done term by term?
Yes, you would have to find and prove the general term of that series ( done by induction ). Once you have the general term it is easy to see all terms after the constant term have an x in them and therefore zero out.
Oh wait, I see what you are saying! Good point. Even the f(0) could be a problem.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#113 2011-07-01 00:10:25
- gAr
- Star Member
Offline
Re: Limits!
Hi,
Yes!
That's why I avoided giving that in my solution.
I thought maybe we can use binomial theorem, but that too fails. (or is it me?)
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#114 2011-07-01 00:13:47
- bobbym
- Administrator
Online
Re: Limits!
Hi gAr;
That is one way, maybe.
Also this is like a piece of experimental math. You use a package to get the answer and then you prove the answer is correct by induction. Sort of like the more classical use of guessing at the solution of a sum or a recurrence.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#115 2011-07-01 00:20:46
- gAr
- Star Member
Offline
Re: Limits!
Hi bobbym,
Yes, I agree.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#116 2011-07-01 00:32:51
- bobbym
- Administrator
Online
Re: Limits!
Hi;
In this case since proving the answer you get is going to be difficult at least from what I see, I think it is easier to use your way.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#117 2011-07-01 00:40:56
- gAr
- Star Member
Offline
Re: Limits!
Hi bobbym,
I think so. From what I know, no other tricks I can think of.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#118 2011-07-02 02:43:37
- anonimnystefy
- Real Member
Offline
Re: Limits!
hi gAr
how about a hint on the 10?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#119 2011-07-02 02:52:07
- gAr
- Star Member
Offline
Re: Limits!
Hi anonimnystefy,
It's already solved in #94.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#120 2011-07-02 03:13:10
#121 2011-07-02 03:19:14
- anonimnystefy
- Real Member
Offline
Re: Limits!
hi 123ronnie123
how did you get the next to last line?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#122 2011-07-02 03:23:14
- 123ronnie321
- Full Member
Offline
Re: Limits!
Hi anonimnystefy,
I am unsure about the ending of my solution and I am waiting for either gAr's or Bobbym's help.
#123 2011-07-02 03:43:54
- gAr
- Star Member
Offline
Re: Limits!
Hi 123ronnie321,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#124 2011-07-02 04:12:25
#125 2011-07-02 13:01:09
- gAr
- Star Member
Offline
Re: Limits!
Hi,
You're welcome!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."