indeterminate

Examples of indeterminate in the following topics:

• Indeterminate Forms and L'Hôpital's Rule

  • Indeterminate forms like $\frac{0}{0}$ have no definite value; however, when a limit is indeterminate, l'Hôpital's rule can often be used to evaluate it.
  • Occasionally in mathematics, one runs across an equation with an indeterminate form as seen in .
  • The most common example of an indeterminate form is $\frac{0}{0}$.
  • That is why the expression $\frac{0}{0}$ is indeterminate.
  • For example, $\lim_{x\to 0}\frac{x}{x}$ is indeterminate.

• Calculating Limits Using the Limit Laws

  • L'Hôpital's rule (pronounced "lope-ee-tahl," sometimes spelled l'Hospital's rule with silent "s" and identical pronunciation), also called Bernoulli's rule, uses derivatives to help evaluate limits involving indeterminate forms.
  • Application (or repeated application) of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit.

• Finding Limits Algebraically

  • In each case above, when the limits on the right do not exist (or, in the last case, when the limits in both the numerator and the denominator are zero), the limit on the left, called an indeterminate form, may nonetheless still exist—this depends on the functions f and g.
  • Indeterminate forms—for instance, $\frac{0}{0}$, $0 \cdot$ some number, $\infty$, and $\frac{\infty}{\infty}$ are also not covered by these rules, but the corresponding limits can often be determined with L'Hôpital's rule or the squeeze theorem.