Asymptotes and Limits at Infinity

AP Calculus AB· difficulty 2/5

Evaluate limx2x31x2+5x\displaystyle\lim_{x \to \infty}\dfrac{2x^3 - 1}{x^2 + 5x}.

  • A

    \infty

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  • B

    00

  • C

    22

  • D

    -\infty

Explanation

Numerator degree 33 > denominator degree 22. As xx \to \infty, leading term 2x32x^3 dominates → ++\infty.

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