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Thread: Limits challenge, can someone tell me how to calculate it?

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    Limits challenge, can someone tell me how to calculate it?

    Limits challenge, can someone tell me how to calculate it?-capture20180403222321017.png
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    Re: Limits challenge, can someone tell me how to calculate it?

    Quote Originally Posted by luiza001 View Post
    Click image for larger version. 

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    You can use l'hopital's rule twice or factor out x-1 from the the numerator and denominator.
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    Re: Limits challenge, can someone tell me how to calculate it?

    Quote Originally Posted by JaguarXJS View Post
    You can use l'hopital's rule twice or factor out x-1 from the the numerator and denominator.
    Actually just apply L'Hopital once (or factor out the $(x-1)$ as suggested).
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    Re: Limits challenge, can someone tell me how to calculate it?

    Quote Originally Posted by JaguarXJS View Post
    You can use l'hopital's rule twice or ....
    You cannot use it twice, because after the first use, the expression is no longer an indeterminate form.


    Quote Originally Posted by JaguarXJS View Post
    ... factor out x-1 from the numerator and denominator.
    Can you do the factorization without involving (read: writing out) dozens of terms in both the numerator and denominator?
    Last edited by greg1313; Apr 4th 2018 at 06:32 AM.
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    Re: Limits challenge, can someone tell me how to calculate it?

    Quote Originally Posted by greg1313 View Post
    You cannot use it twice, because after the first use, the expression is no longer an indeterminate form.
    That is the whole point of l'H˘pital's rule.
    $\displaystyle{{\lim _{x \to 1}}\dfrac{{{x^{100}} - 2x + 1}}{{{x^{50}} - 2x + 1}}\mathop = \limits^H {\lim _{x \to 1}}\dfrac{{100{x^{99}} - 2}}{{50{x^{49}} - 2}}} = ?$
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