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L'Hôpital's Rule

AP Calculus AB· difficulty 3/5

Evaluate lim⁡x→1(1x−1−1ln⁡x)\displaystyle\lim_{x\to 1}\left(\dfrac{1}{x-1} - \dfrac{1}{\ln x}\right).

  • A

    12\tfrac{1}{2}

  • B

    Does not exist

  • C

    00

  • D

    −12-\tfrac{1}{2}

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Explanation

Combine: (ln⁡x−(x−1))/((x−1)ln⁡x)(\ln x - (x-1))/((x-1)\ln x). Apply L'Hôpital twice → −1/2-1/2.

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