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Calculus · Limits

Limit of 1/(1 - t) as t → 1

\lim_{t \to 1} \frac{1}{1 - t}

Step by step

  1. \lim_{t \to 1^-} \frac{1}{1 - t}

    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_{t\to 1^-} = \infty,\quad \lim_{t\to 1^+} = -\infty

    One-sided limits.

Reveal the answer
\infty