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#1 2012-11-07 18:49:37
- princess snowwhite
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finding limit
((1+cx)/(1-cx))^(1/x) tends to 4 as x tends to infinity.
find the limit of ((1+2cx)/(1-2cx))^(1/x) as x tends to infinity.
#2 2012-11-07 19:41:28
- bobbym
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Re: finding limit
Hi princess snowwhite;
For the first part of the question:
((1+cx)/(1-cx))^(1/x) tends to 4 as x tends to infinity.
I can not find any c that will give 4 as x approaches infinity.
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.
#3 2012-11-08 00:46:26
- anonimnystefy
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Re: finding limit
The first limit is 1 for every c.
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
#4 2012-11-08 05:21:06
- bobbym
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Re: finding limit
Hi;
That is what I am getting, so the question does not make any sense.
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.
#5 2012-11-08 06:20:27
- anonimnystefy
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Re: finding limit
Maybe it is a misprint or a typo.
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
#6 2012-11-08 06:27:03
- bobbym
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Re: finding limit
Yes, it should read 1 instead of 4.
find the limit of ((1+2cx)/(1-2cx))^(1/x) as x tends to infinity
So the answer should be 1 because 2c=c.
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.
#7 2012-11-08 07:25:20
- anonimnystefy
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Re: finding limit
I don't think that is the misprint.
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
#8 2012-11-08 07:33:30
- bobbym
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Re: finding limit
But doesn't it follow?
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.
#9 2012-11-08 07:36:30
- anonimnystefy
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Re: finding limit
Not really. The question would be close to trivial. I think the question is more likely to be asking for the constant c for which a limit has the value 4 and then finding the same limit but with 2c instead of the c, whose value we now know.
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
#10 2012-11-08 07:40:18
- bobbym
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Re: finding limit
anonimnystefy wrote:
The first limit is 1 for every c.
There is no c that will give a limit of 4. You said so yourself. The limit is independent of c. That is why it is trivial.
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.
#11 2012-11-08 07:45:48
- anonimnystefy
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Re: finding limit
Yes. So I am thinking that it might be a typo of the function whose limit is being taken.
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
#12 2012-11-08 07:48:42
- bobbym
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Re: finding limit
Maybe the questioner just wants the OP to see that the answer is 1. To spot the inconsistency.
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.
#13 2012-11-08 07:53:17
- anonimnystefy
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Re: finding limit
This looks too much like a book problem. I do not think that is what it wants.
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
#14 2012-11-08 07:55:33
- bobbym
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Re: finding limit
Isn't the simplest typo that she wrote 4 when she meant 1?
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.
#15 2012-11-08 08:00:10
- anonimnystefy
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Re: finding limit
Being simplest doesn't makng true. And, yes, I am familiar with the Occam's razor.
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
#16 2012-11-08 08:01:57
- bobbym
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Re: finding limit
I use Schick's or Gillette's razor for a better shave.
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.
#17 2012-11-13 01:26:50
- mathteacher005
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Re: finding limit
Hello! The answer is \lim_{x\to\infty }\left({{2\,{\it cx}+1}\over{1-2\,{\it cx}}}\right)^{{{1}\over{x}}} = 1.
You can check it here.
numberempire.com/limitcalculator.php?function=%28%281%2B2%2Acx%29%2F%281-2%2Acx%29%29%5E%281%2Fx%29&var=x&val=inf&answers=&limit_type=two-sided
My friend show me few weeks ago and now my students always use it for checking the answers:) Good Luck!
#18 2012-11-13 05:29:24
- bob bundy
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Re: finding limit
hi mathteacher005
Welcome to the forum and thanks for the link.
I will convert your post so that the expression is in Latex and the link easier to use.
numberempire.com/limitcalculator.php?fu … =two-sided
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei