Re: TIB: What e is

To: ti-basic@lists.ticalc.org
Subject: Re: TIB: What e is
From: "Zane Tian" <arkane17@hotmail.com>
Date: Sat, 25 Mar 2000 19:22:59 EST
Reply-To: ti-basic@lists.ticalc.org

That was a GREAT novel =)  You explained it really really well.  (I'm sure 
your math teacher would be proud)  Since I haven't dealt with calculus yet, 
I have no idea of the significance of the derivative and integral being the 
same.  Ah well. =)

>From: KeysDezez@cs.com
>Reply-To: ti-basic@lists.ticalc.org
>To: ti-basic@lists.ticalc.org
>Subject: TIB: What e is
>Date: Thu, 23 Mar 2000 19:35:41 EST
>
>
>     e is the constant such that the derivative of e^x with respect to x is 
>is
>e^x.  What this means is basically that the slope of the the curve e^x at 
>the
>point (x,e^x) is equal to e^x.  That might not sound like much but it's a 
>big
>deal.  Of course, this means that the integral of e^x with respect to x is
>also e^x.
>
>     e is equal to the limit as x approaches infinity of (1+1/x)^x.  That
>means that the larger the number you plug in for x, the closer (1+1/x)^x is
>to e.  e is approximately equal to 2.718281828459.  Some more interesting
>facts about e:
>
>e^(xi) = cis(x)
>In case you don't know, i = sqrt(-1) and cis(x) = cos(x)+sin(x)*i
>
>As a result of the previous statement,
>e^(pi*i) = -1
>
>Another similar fact:
>e^(-pi/2) = i^i
>
>The opposite of doing e^x is ln(x).  ln is the natural log or log base e.
>That means that the following two statements are equivalent:
>
>e^x = y
>ln y = x
>
>The derivative of ln(x) with respect to x is 1/x.  The integral of ln(x) 
>with
>respect to x is x*ln(x) - x.
>
>e is most often used in problems of exponential growth and decay.  An 
>example
>of such a problem is a half-life problem.  (Which are usually easier easier
>withour using e.  It's just an example of the type of problem.)
>
>e, in short is one of the most important transidential numbers.  Other
>important numbers of this kind include pi, phi, psi, and sqrt(2).
>
>I probably just told you a whole lot more than you wanted to know.  I just
>love number theory, don't you?  If anyone would like me to go on, tell me.
>Otherwise, I think I should shut up now...
>
>This concludes yet another edition of "Grant Babbles Meaninglessly."
>
>
>
>In a message dated 3/23/00 2:36:23 PM Eastern Standard Time, 
>HaRMaN10@aol.com
>writes:
>
> > Ok i got to thinking during math class the other day and i was wondering
>what
> >
> >  is up with this e number thing.  Could someone explain that to me?
>

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