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Math Help - Series and sequences

  1. #1
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    Series and sequences

    Show that f(x) = (x^3 + 1)/(x - 7) is order  x^2
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by racewithferrari View Post
    Show that f(x) = (x^3 + 1)/(x - 7) is order  x^2
    I'm sorry. What does order mean?
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  3. #3
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    I don't know but my prof said that start by considering (x-7)f(x) and use theorems on the combination of functions.
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by racewithferrari View Post
    I don't know but my prof said that start by considering (x-7)f(x) and use theorems on the combination of functions.
    What makes sense is to say that f(x)=\mathcal{O}\left(x^2\right) or that \lim_{x\to\infty}\frac{f(x)}{x^2}=c for some c\in\mathbb{R}. Does that sound feasible?
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  5. #5
    MHF Contributor chisigma's Avatar
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    The 'division' between polynomials can be performed as...

    f(x)=\frac{x^{3}+1}{x-7} = \frac{x^{3}-7x^{2}}{x-7} + \frac{7x^{2} +1}{x-7}=

    = x^{2} + \frac{7x^{2}-49x}{x-7} + \frac{49x+1}{x-7}=

    = x^{2} +7x + \frac{49x-343}{x-7} + \frac{344}{x-7}= x^{2} + 7x + 49 + \frac{344}{x-7}

    ... so that is...

    f(x)= \mathcal{O} \{x^{2}\}

    Kind regards

    \chi \sigma
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