TIB: What e is
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TIB: What e is
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?