maths.free › Calculus › Limits

Limits

Substitution, factoring and L'Hôpital's rule.

A limit asks what a function approaches, not what it equals. Try substitution first; if it gives 0/0, factor and cancel, or differentiate top and bottom (L'Hôpital). The graph shows the function near the point with the limit marked.

Arbejdstxrd eksempel: limit of sin(x)/x as x -> 0

Calculus · Limits

Limit of sin(x)/x as x → 0

\lim_{x \to 0} \frac{\sin{\left(x \right)}}{x}

Trin for trin

  1. \lim_{x \to 0^+-} \frac{\sin{\left(x \right)}}{x}

    Try direct substitution first.

  2. \frac{0}{0}

    Substitution gives 0/0 — an indeterminate form.

  3. \lim \frac{\cos{\left(x \right)}}{1}

    L'Hôpital's rule: differentiate numerator and denominator separately.

  4. = 1

    Substitute.

Afslør svaret
1

Prøv din egen

Mere i Calculus

DerivativesIntegralsDefinite integralsTaylor seriesSeries and sumsMaxima and minima