Limits that equal e
Ah, yes, this seems like the most famous mathematical term, I have heard before. I was looking at a function whose limit was e as it went to infinity, so I decided to read up about this sort of thing, and found out how amazing e really is, went on a few hour rant reading various things about it. never really clicked before . Now my question is, if you given a limit say and it contains some sort of ratio/fraction where n is in the denominator and involves something to the nth power, this is an observation I made, which, of course in math, can get you somewhere very wrong, the observation that if the function contains something along the lines of what I just suggested it will go to a limit equivalent to e?
as I was suggested this example earlier by redsox apart from the traditional "definition" of e
Think of it this way.
ln of both sides:
According to the basic property of exponential...
... so that it is not necessary that ...
So this would work for this limit as well.
Originally Posted by chisigma
by the property of the exponentional you stated
would that still hold true? forgot the power of n, but you catch my drift
. Informally is much too "strong". It will completely overpower the base. I mean there are many more limits that give . One that is not particularly interesting but comes to mind is .
Yes, would the function I just suggested go to infinity? after I had time to work it out I got
Originally Posted by Drexel28