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Asymptotes and Limits at Infinity

AP Calculus AB· difficulty 4/5

lim⁡x→∞4x2+53x−1=\displaystyle \lim_{x \to \infty} \frac{\sqrt{4x^2 + 5}}{3x - 1} =

  • A

    23\frac{2}{3}

    check_circle
  • B

    43\frac{4}{3}

  • C

    22

  • D

    Does not exist

Explanation

For x→∞x \to \infty, 4x2+5/(3x)→2/3\sqrt{4x^2+5}/(3x) \to 2/3. So lim⁡=4/3=2/3\lim = \sqrt{4}/3 = 2/3.

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