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L'Hôpital's Rule

AP Calculus AB· difficulty 3/5

Evaluate lim⁡x→0+xln⁡x\displaystyle\lim_{x\to 0^+} x \ln x.

  • A

    00

    check_circle
  • B

    11

  • C

    −1-1

  • D

    −∞-\infty

Explanation

Rewrite as ln⁡x/(1/x)\ln x/(1/x), ∞/∞\infty/\infty at x→0+x \to 0^+? Actually −∞/∞-\infty/\infty. L'Hôpital: (1/x)/(−1/x2)=−x→0(1/x)/(-1/x^2) = -x \to 0.

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