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Limits problem

  1. Aug 16, 2010 #1
    1. The problem statement, all variables and given/known data
    [PLAIN]http://img517.imageshack.us/img517/2516/62548919.jpg [Broken]


    I'm hopeless to solve this problem
    you can give me a hint before solving the problem!
    Thanks in advance
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 16, 2010 #2

    Mark44

    Staff: Mentor

    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.
     
  4. Aug 16, 2010 #3
    still can't solve it ...we can factorize the numerator but still makin no sense....Can u make it simpler?
     
    Last edited: Aug 16, 2010
  5. Aug 16, 2010 #4
    Did you try L'Hopital's rule?

    Can you post your work?
     
  6. Aug 16, 2010 #5

    Mark44

    Staff: Mentor

    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]
     
  7. Aug 16, 2010 #6
    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 :(
     
  8. Aug 16, 2010 #7
    Well, if you use Mark44's substitution you wont need to use L'Hopital's rule
     
  9. Aug 16, 2010 #8

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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".
     
  10. Aug 16, 2010 #9
     
  11. Aug 17, 2010 #10

    hunt_mat

    User Avatar
    Homework Helper

    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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