Someone posted it here a few days ago but got no answers:
http://www.mathhelpforum.com/math-he...expansion.html
The answer still eludes me.
Hey Gang:
Here is a limit I saw somewhere recently but can not remember where. I think on another site.
Anyway, the restrictions are no expansions on e, no binomial expansion on the radical term and no L'Hopital. Go figure.
I just thought it'd be cool to see some clever ways folks come up with.
Someone posted it here a few days ago but got no answers:
http://www.mathhelpforum.com/math-he...expansion.html
The answer still eludes me.
By taking derivatives we can prove on we have:
(These inequalities are inspired by Talyor's theorem but they make no mention of the theorem).
Uses these inequalities we can squeeze the function. The limit is completed by rationalizing the numerator. Here is an illustration with the lower bound.
Now this is,
When we expand the trinomial we get
After canceling and dividing by and ingoring higher degree terms we get as a lower bound.
Now do the same thing with the second polynomial.