Re: virus: maxims and ground rules and suppositions

the great tinkerer (
Thu, 13 May 1999 14:20:20 PDT

>e -- useful in calculus; equals
> lim (1+x)^(1/x) = lim (1+ 1/x)^x
> x -->0 x --> infinity
> and (here's the kicker...) diff(e^x, x) = e^x

lets see how good my memory is:
i like e... ;-)
i = (-1)^(1/2) (imaginary unit)
e^(ix) = cos x + i(sin x) (so e^(iPi) = -1) e can also be expressed as the summation of 1/n! index n=0 limit infinity e^x is the summation of x^n/n! index n=0 limit infinity therefore if you take e^(ix) the real terms will be only the even n's imaginaries will be all the odd terms.
real (e^(ix)) = summation of ((-1)^(n+1)(x)^(2n))/(2n)! (index n=0 and limit infinity)
imag (e^(ix)) = summation or ((-1)^(n)(x)^(2n-1))/(2n-1)! (index n=0 and limit infinity)
cos x = summation ((-1)^(n+1)(x)^(2n))/(2n)! (index n=0 limit inf) sin x = summation ((-1)^(n)(x)^(2n-1))/(2n-1)! (index n=0 limit inf)

and that is how i choose to define sine and cosine functions...

~the great tinkerer

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