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Calculus · Limits

Limit of (2x^2 + 1)/(x^2 - 3) as x → oo

\lim_{x \to \infty} \frac{2 x^{2} + 1}{x^{2} - 3}

Step by step

  1. \lim_{x \to \infty^+-} \frac{2 x^{2} + 1}{x^{2} - 3}

    Try direct substitution first.

  2. \

    As x grows without bound, compare the fastest-growing terms (or divide top and bottom by the highest power).

  3. \frac{2 + \frac{1}{x^{2}}}{1 - \frac{3}{x^{2}}}

    Divide numerator and denominator by x^2.

  4. = 2

    Take the limit.

Reveal the answer
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