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Math Help - derivation of a limit problem .. algebra help needed!

  1. #1
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    derivation of a limit problem .. algebra help needed!

    Hello all,

    I am trying to understand whats going on algebra wise here,

    (6n^4+2n^3) / (7n-11^4)

    from here i needed to eliminate the n^4 terms, so;

    ((6n^4+2n^3) / (7n-11^4)) * (1/n^4)/(1/n^4) ..

    so far so good, but apparantly this all then simplifies to :

    (6+(2/n))/((7/n^3)-11)

    I cannot work out how we arrive at this answer.

    Help would be greatly appreciated,

    kind thanks
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  2. #2
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    Re: derivation of a limit problem .. algebra help needed!

    You are finding the limit as n → what?
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  3. #3
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    Re: derivation of a limit problem .. algebra help needed!

    i know that 2/n and 7/n^3 tend to zero; given by the reciprocal rule, thus this problem converges to 6/-11 . i get the final answer, its the algebra manipulation beforehand thats bothering me.


    thanks
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  4. #4
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    Re: derivation of a limit problem .. algebra help needed!

    Quote Originally Posted by euphmorning View Post
    i know that 2/n and 7/n^3 tend to zero; given by the reciprocal rule, thus this problem converges to 6/-11 . i get the final answer, its the algebra manipulation beforehand thats bothering me.
    Look! The point is the expression (6n^4+2n^3) / (7n-11^4) is very hard to read.
    The limit as n\to \infty of that is \infty.
    So I think you have posted something you don't want.
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  5. #5
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    Re: derivation of a limit problem .. algebra help needed!

    my problem was concerned with understanding the algebra manipulation. sorry if my problem has inadvertantly confused .
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  6. #6
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    Re: derivation of a limit problem .. algebra help needed!

    is this the expression you're dealing with?

    \frac{6n^4+2n^3}{7n-11n^4}

    are you trying to find the limit as n \to \infty ?

    if so, take care in proofing your post.
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    Re: derivation of a limit problem .. algebra help needed!

    Quote Originally Posted by skeeter View Post
    is this the expression you're dealing with?

    \frac{6n^4+2n^3}{7n-11n^4}

    are you trying to find the limit as n \to \infty ?

    if so, take care in proofing your post.
    That is clearly not OP.

    It was \frac{6n^4+2n^3}{7n-11^4}

    That is why I asked for a clarification!
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  8. #8
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    Re: derivation of a limit problem .. algebra help needed!

    Quote Originally Posted by skeeter View Post
    is this the expression you're dealing with?

    \frac{6n^4+2n^3}{7n-11n^4}

    are you trying to find the limit as n \to \infty ?




    if so, take care in proofing your post.

    thanks, yes thats the expression i'm dealing with; as n goes to infinity.
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  9. #9
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    Re: derivation of a limit problem .. algebra help needed!

    Yes, so one thing you could do is divide the numerator and the demoninator by n^4.

    This would leave you with (6 + 2/n)/(7/n^3 - 11)

    now as n approaches infinity, the numerator approaches 6. This is because, as n approaches infinity, 2/n goes to 0.
    and also, as n approaches infinity, the denominator approaches -11. This is because, as n approaches infinity 7/n^3 also approaches 0.

    and hence you are left with 6 in the numerator and -11 in the demoninator, and thus the limit as n approaches infinity is -6/11

    oh that wasn't the original post, but if that's what was intended then there you go
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  10. #10
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    Re: derivation of a limit problem .. algebra help needed!

    \displaystyle \begin{align*} \frac{6n^4 + 2n^3}{7n - 11n^4} &= \left(\frac{6n^4 + 2n^3}{7n - 11n^4}\right) \left(\frac{\frac{1}{n^4}}{\frac{1}{n^4}}\right) \\ &= \frac{\frac{1}{n^4}(6n^4 + 2n^3)}{\frac{1}{n^4}(7n - 11n^4)} \\ &= \frac{\frac{6n^4}{n^4} + \frac{2n^3}{n^4}}{\frac{7n}{n^4} - \frac{11n^4}{n^4}} \\ &= \frac{6 + \frac{2}{n}}{\frac{7}{n^3} - 11} \end{align*}

    Now make \displaystyle n \to \infty.
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    Re: derivation of a limit problem .. algebra help needed!

    thanks, that neat break down really has helped. i'm just stuck with how you reach the last part. i think this is just some basic algebra i'm not quite getting! ie. where does the 2/n and 7/n^3 expressions come from?
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    Re: derivation of a limit problem .. algebra help needed!

    Quote Originally Posted by euphmorning View Post
    thanks, that neat break down really has helped. i'm just stuck with how you reach the last part. i think this is just some basic algebra i'm not quite getting! ie. where does the 2/n and 7/n^3 expressions come from?
    What is \displaystyle \frac{n^3}{n^4} equal to? \displaystyle \frac{n^3}{n^4} = \frac{n\cdot n\cdot n}{n\cdot n \cdot n \cdot n} = \frac{1}{n}.

    It's basic index laws, \displaystyle \frac{n^a}{n^b} = n^{a-b}
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  13. #13
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    Re: derivation of a limit problem .. algebra help needed!

    Thats making perfect sense now. many thanks!
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