Solving a Problem I'm Hopeless With: A Hint Needed!

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Homework Help Overview

The discussion revolves around a limit problem involving the expression \(\lim_{n \to \infty}\frac{(A + (1/n))^4 - A^4}{1/n}\). Participants are exploring various approaches to tackle this limit, particularly focusing on the application of L'Hopital's Rule and alternative methods of simplification.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants suggest rewriting the limit expression and applying L'Hopital's Rule, while others express uncertainty about this method due to a lack of prior knowledge. There are discussions about factorization and expansion of the expression to simplify the problem.

Discussion Status

The conversation is ongoing, with various hints and suggestions provided. Some participants are questioning the original poster's understanding and encouraging them to share their work. There is a mix of advice on different approaches, but no consensus has been reached on a single method to solve the problem.

Contextual Notes

There is a noted concern regarding the original poster's unfamiliarity with L'Hopital's Rule, which has implications for their ability to engage with the problem as presented. Additionally, the original poster expresses frustration with their own attempts, indicating a struggle with the material.

Misr
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Homework Statement


[PLAIN]http://img517.imageshack.us/img517/2516/62548919.jpg


I'm hopeless to solve this problem
you can give me a hint before solving the problem!
Thanks in advance
 
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You might try rewriting this as
[tex]\lim_{n \to \infty}\frac{(A + (1/n))^4 - A^4}{1/n}[/tex]

In this form, the expression has the indeterminate form [0/0], so you can use L'Hopital's Rule on it.
 
still can't solve it ...we can factorize the numerator but still makin no sense...Can u make it simpler?
 
Last edited:
Did you try L'Hopital's rule?

Can you post your work?
 
Do you know how to use L'Hopital's Rule?

A slightly different approach is this, with h = 1/n
[tex]\lim_{h \to 0^+}\frac{(A + h)^4 - A^4}{h}[/tex]
 
No...I don't know anything about this rule we don't study it at school and they can't give us a problem on a rule which we haven't studied yet :(
 
Well, if you use Mark44's substitution you won't need to use L'Hopital's rule
 
You need to show us what work you have done on the problem, Misr, even if it's just thoughts about it. It is unacceptable to just post a question and say "I can't do it".

And a reminder for homework helpers: our goal is to help posters do a problem, not to give them answers. The OP has gotten plenty of advice, and his own idea that he didn't post the work for sounds like a very workable approach too. If he doesn't start showing that he's done anything with any of that, then it is inappropriate to give further "help".
 
You need to show us what work you have done on the problem, Misr, even if it's just thoughts about it. It is unacceptable to just post a question and say "I can't do it".
[/quoye]
Yep, I totally agree and I DO respect this ...but my work is very random and terrible and it has nothin to do with the right answer...I tried your creative ways before..so I agree with that ...it gives excellent results
hope you can understand this
Thanks very much
 
  • #10
Have you tried expanding:
[tex] (A+n^{-1})^{4}=A^{4}+4\frac{A^{3}}{n}+6\frac{A^{2}}{n^{2}}+4\frac{A}{n^{3}}+\frac{1}{n^4}[/tex]
I think that this will solve your problem.
 

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