Re: TIB: What e is
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Re: TIB: What e is
You can keep babbling.. i learn more from reading your mails than i do in my
math class.
-jordan
> 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."