Asymptotes and Limits at Infinity

AP Calculus AB· difficulty 2/5

Evaluate limx5x3+1x32x\displaystyle\lim_{x \to -\infty}\dfrac{5x^3 + 1}{x^3 - 2x}.

  • A

    55

    check_circle
  • B

    5-5

  • C

    -\infty

  • D

    00

Explanation

Same degree: ratio of leading coefficients = 5/1=55/1 = 5 regardless of x±x \to \pm\infty.

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