L'Hôpital's Rule

AP Calculus AB· difficulty 2/5

Evaluate limx0ex1xx2\displaystyle\lim_{x\to 0}\dfrac{e^x - 1 - x}{x^2}.

  • A

    11

  • B

    12\tfrac{1}{2}

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  • C

    00

  • D

    22

Explanation

L'Hôpital twice: (ex1)/(2x)ex/21/2(e^x - 1)/(2x) \to e^x/2 \to 1/2.

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