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.

• Factors that Shift Demand and Supply Functions

  • When the supply and demand both shift, either the market quantity or price becomes indeterminate.
  • In this case, market price increases while market quantity becomes indeterminate.
  • We can use a trick to determine which variable becomes indeterminate.
  • Consequently, one variable always moves in one direction while the other can increase and decrease, making it indeterminate.
  • In this case, the equilibrium quantity for U.S. dollars becomes 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.

• Arches and Domes

  • Because it is subject to additional internal stress caused by thermal expansion and contraction, this type of arch is considered to be statically indeterminate.
  • Because the structure is pinned between the two base connections, which can result in additional stresses, the two-hinged arch is also statically indeterminate, although not to the degree of the fixed arch.

• Interest Rates and the Business Cycle

  • When both the supply and demand functions shift, we know either the price or quantity while the other variable becomes indeterminate.

• Answers to Chapter 8 Questions

  • Quantity is determinate while bond prices, and thus bond interest rates are indeterminate.

• Qualities of Line

  • Meandering lines can be either geometric or expressive, and one can see how their indeterminate paths animate a surface to different degrees.

• Market Adjustment to Change

  • When supply and demand both change, the direction of the change of either equilibrium price or quantity can be known but the effect on the other is indeterminate.
  • When supply and demand both shift, the direction of change in either equilibrium price or quantity can be known but direction of change in the value of the other is indeterminate.

• Spectrum of Antimicrobial Activity

  • While Gram staining is a valuable diagnostic tool in both clinical and research settings, not all bacteria can be definitively classified by this technique, thus forming Gram-variable and Gram-indeterminate groups as well.