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Homework Help: What is the limit for cos (n pi) and sin (n pi)?

  1. Feb 14, 2006 #1
    may i know how to solve [ n^2 cos(n(pi)) ]/ n^2 + 42??

    i have divided it by n^2 and get cos(n pi) / (42/n^2) and i can't solve already.pls help

    what is the limit for cos (n pi) and sin (n pi)??
     
  2. jcsd
  3. Feb 14, 2006 #2

    TD

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    Please use latex or make the expressions more clear, using paranthesis since a/b+c isn't the same as a/(b+c), you see?
    Also, the limit for what (of course n here) going to what?

    I'm guessing you mean the something which looks like

    [tex]\mathop {\lim }\limits_{n \to ?} \frac{{n^2 \cos \left( {n\pi } \right)}}{{n^2 + 42}}[/tex]
     
    Last edited: Feb 14, 2006
  4. Feb 14, 2006 #3
    [ n^2 cos(n pi ) ] / (n^2 + 42) for n >1

    what is the limit for cos (n pi) and sin (n pi) for n>1 also??
     
  5. Feb 14, 2006 #4

    TD

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    Again, the limit of those expressions for n going to what? To 0, pi, infinity, ...? You can't say "the limit for n>1"...
     
  6. Feb 14, 2006 #5
    oh...yaya for n to infinity
     
  7. Feb 14, 2006 #6

    TD

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    Ah :smile:

    In that case, the limit doesn't exist since sin as well as cos will keep oscilating between -1 and 1.
     
  8. Feb 14, 2006 #7
    Except for sin(n pi) which is identically zero for all n.
     
  9. Feb 14, 2006 #8

    TD

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    That's only true for integer values of n, we're letting n go to infinity here.
     
  10. Feb 14, 2006 #9
    so,what is the answer for my first question??
     
  11. Feb 14, 2006 #10

    TD

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    The answer to this?

    [tex]\mathop {\lim }\limits_{n \to +\infty} \frac{{n^2 \cos \left( {n\pi } \right)}}{{n^2 + 42}}[/tex]

    The limit doesn't exist for the reason I gave above.
     
  12. Feb 14, 2006 #11
    True, but I had always been taught that if you have a limit as "n" goes to infinity, then you are talking about integer values for "n". If you want all values, then you use "x" instead of n. Hence, the reason I made the statement.
     
  13. Feb 14, 2006 #12
    is it possible to obtain an answer if n goes to 1 ??
     
  14. Feb 14, 2006 #13

    TD

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    Sure, just fill in n = 1.
     
  15. Feb 14, 2006 #14

    matt grime

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    Gah, shake head, look askance. limit as n goes to 1..... n is taken to be integer valued, it makes no sense to ask 'as n tends to 1'. See Daveb's very important interjection, TD.
     
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