A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Norm Goldblatt
Date: 2015 Mar 21, 00:31 -0700
As an ex-teacher, I would take points off for not showing your work. Your answer is correct, but you don't explain how 0/0 can be defined. One way out of this dilemma is by invoking L'Hospital's rule (one of my favorite rules!) which says that the ratio of the limits of the derivatives is the same as the ratio of the functions themselves (in cases when lim is either 0/0 or inf/inf). So, lim sin x/x= cosx/1=1/1=1. But then we know (without proof here- yeah, you should take off points) that sinx approaches x as x gets smaller and smaller.
But back to the original question- What a wonderful and curious result. Thanks for posing it.
All this just to prove that this 'lurker' is paying attention and thoroughly enjoying the wonderful conversations.