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Re: ARTICLE : Mathematics in ancient India
> : b) Manjula (432 AD) uses concepts like: (Sin[x-dx]-SIn[x])/dx = 1,
> : if dx approaches zero. Herein we see the roots of modern
> : calculus, which was later developed by Newton and Leibnitz.
>
>
>
> Nope. It goes to -1. I am sure the ghosts of Newton and Leibniz will be
> *very* reassured.
Nope. It actually goes to -cos[x].
I've assumed that the above is identical to:
Sin[x-h] - Sin[x]
lim ----------------- = - cos [x]
h-->0 h
The steps are:
Sin[x-h] - Sin[x] = 2*Sin[(x-h-x)/2]*Cos[(x-h+x)/2]
= 2*sin[-h/2]*Cos[(2x+h)/2]
as h--->0, sin[-h/2] apporximately equals -h/2.
Therefore, the answer is -cosx. Of course, if x=0, it is -1.
-Kartik
