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

2. ## Re: Limits challenge, can someone tell me how to calculate it?

You can use l'hopital's rule twice or factor out x-1 from the the numerator and denominator.

3. ## Re: Limits challenge, can someone tell me how to calculate it? Originally Posted by JaguarXJS 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).

4. ## Re: Limits challenge, can someone tell me how to calculate it? Originally Posted by JaguarXJS 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. Originally Posted by JaguarXJS ... 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?

5. ## Re: Limits challenge, can someone tell me how to calculate it? Originally Posted by greg1313 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'Hôpital's rule.
$\displaystyle{{\lim _{x \to 1}}\dfrac{{{x^{100}} - 2x + 1}}{{{x^{50}} - 2x + 1}}\mathop = \limits^H {\lim _{x \to 1}}\dfrac{{100{x^{99}} - 2}}{{50{x^{49}} - 2}}} = ?$