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Calculus · Limits

Limit of 1/x as x → 0

\lim_{x \to 0} \frac{1}{x}

Step by step

  1. \lim_{x \to 0^+} \frac{1}{x}

    Try direct substitution first.

  2. \frac{1}{0}

    The denominator goes to 0 while the numerator does not. Look at the sign from each side.

  3. \lim_{x\to 0^-} = -\infty,\quad \lim_{x\to 0^+} = \infty

    One-sided limits.

Reveal the answer
\infty