What does indeterminate form mean exactly? Does it just mean that you can't determine an answer?
http://mathworld.wolfram.com/Indeterminate.html
Thank you.
You're welcome, John.
An indeterminate form is a mathematical expression that cannot be evaluated directly using basic rules or techniques. It does not mean that you cannot determine an answer, but rather that additional steps are required to find a meaningful result. These expressions typically involve dividing one quantity by another, where both quantities approach certain limiting values, such as zero divided by zero or infinity divided by infinity.
The term "indeterminate" comes from the fact that it is not possible to determine the exact value of the expression without further analysis. In such cases, additional mathematical tools such as limit theorems, differentiation techniques, or other advanced methods are used to determine the behavior of the expression and find a solution.
Indeterminate forms are encountered in various branches of mathematics, particularly in calculus and analysis. They often arise when dealing with limits, derivatives, integrals, or series. Examples of indeterminate forms include 0/0, ∞/∞, 0 × ∞, ∞ − ∞, and 1^∞, among others.
To evaluate an indeterminate form, one needs to apply specific techniques such as L'Hôpital's rule, the limit properties, or algebraic manipulations to transform the expression into a form that can be evaluated. These techniques aim to simplify the expression or transform it into a known form for which the limit can be determined.
Overall, indeterminate forms represent situations where more analysis is required to determine the answer, rather than indicating that an answer cannot be determined at all.