Asymptotes and Limits at Infinity

AP Calculus AB· difficulty 3/5

Evaluate limx4x2+12x+3\displaystyle\lim_{x\to\infty}\dfrac{\sqrt{4x^2 + 1}}{2x + 3}.

  • A

    00

  • B

    11

    check_circle
  • C

    22

  • D

    12\tfrac{1}{2}

Explanation

For large x>0x > 0: 4x2+12x\sqrt{4x^2+1} \approx 2x. Dominant terms: 2x/(2x)=12x/(2x) = 1.

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