This is the third post regarding the notion of asymptotic comparison. The first one dealt with equivalents, the rigorous way of saying "these two things look alike", while the second post was about little o, meaning "this thing is much smaller than this other one". Naturally, where there is a little o, there should be … Continue reading Asymptotic comparison – III
Tag: hospital rule
Asymptotic comparison – II
This is the second post regarding the notion of asymptotic comparison. The first one dealt with equivalents, the rigorous way of saying "these two things look alike". This post is about little o, which describes what we mean by "this thing is much smaller than this other one". Yes, the "o" is the letter o, … Continue reading Asymptotic comparison – II
Asymptotic comparison – I
In the coming posts, I want to discuss the notions of asymptotic comparison, which is essentially the mathy way of saying "these two things look alike" or "this one is much larger than this other one". The point, as with many new notions, is to simplify. Most of the expressions / formulas / functions that … Continue reading Asymptotic comparison – I
L’Hospital rule
I had never heard of L'Hospital rule before I had to teach it, one fateful morning of 2012 at the University of Toronto. The class was your standard Calculus 1 class, where L'Hospital rule features prominently as your one-size-fits-all trick to compute limits. "How come I never heard of this?", I thought. That's when I … Continue reading L’Hospital rule
Let epsilon be positive 