Indeterminate form: Difference between revisions

Revision as of 01:43, 3 July 2025

Revision as of 10:32, 3 July 2025

Line 140:

Although L'Hôpital's rule applies to both <math>0/0</math> and <math>\infty/\infty</math>, one of these forms may be more useful than the other in a particular case (because of the possibility of algebraic simplification afterwards). One can change between these forms by transforming <math>f/g</math> to <math>(1/g)/(1/f)</math>.

== Confusion around indeterminate forms involving infinity ==

There is confusion surrounding indeterminate forms for laymen and mathematicians with equations that involve infinity. Take the example <math>1^\infty</math>, the rule that <math>1^n=1</math> is a fundamental rule taught since middle school. The reason why mathematicians define the equations below as indeterminate forms is because defining them would cause problems for many systems of mathematics. The intuitive answer would be the correct one. In the example, laymen generally mean <math>\underbrace{ 1*1*1*1*1\cdots*1 }_{\infty}</math> (note that there would be no last 1) which would equal 1. Mathematicians however have a rigorous definition of infinity and with the fact that problems would arise in some fundamental theorems is why equations involving infinity are left as indeterminate.

== List of indeterminate forms ==