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Thread: Limit

  1. #16
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    Re: Limit

    PS: Struggling with this one isn't a sign of "sucking a bit". It's a tough one to get out whichever way you choose.
    Thanks from domy7997 and topsquark
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  2. #17
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    Re: Limit

    Quote Originally Posted by Archie View Post
    PS: Struggling with this one isn't a sign of "sucking a bit". It's a tough one to get out whichever way you choose.
    Okay. Idk how, but now i can read it! Thank you so much... Gonna find out why i got stucked with this limit for so long!
    Huge hug bro!

    Sent from my Redmi Note 4X using Tapatalk
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  3. #18
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    Re: Limit

    Limit-imgtemp_rpvgpt-1.png
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  4. #19
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    Re: Limit

    to simplify the calculations, write

    $\displaystyle \sqrt[3]{\frac{5x^3-x^4}{x-1}}+x=x\left(\sqrt[3]{\frac{5-x}{x-1}}+1\right)$

    and use the substitution

    $\displaystyle y=\sqrt[3]{\frac{5-x}{x-1}}$ so that $\displaystyle x=\frac{y^3+5}{y^3+1}$

    and

    $\displaystyle \sqrt[3]{\frac{5x^3-x^4}{x-1}}+x=\frac{y^3+5}{y^3+1}(y+1)=\frac{y^3+5}{y^2-y+1}$

    now take the limit as $y\to -1$
    Thanks from topsquark
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