Question

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Answer 1

let F be the function
F(x)=y
and f(x) is the derivative of F(x).
so at a point (X,Y) \[y=[-x/f(X)] + F(X) + X/f(X)\]
is a perpendicular
and at point \[(X+ \Delta x, Y+ \Delta y(\Delta x))\]
\[y= [-x/f(X + \Delta x)] + F(X+ \Delta x) + [(X+ \Delta x)/f(X+ \Delta x)]\]
it the perpendicular line.
so solving this lines will give the point \[(X_{0}, Y_{0} )\]
where \[X_{0}=g(\Delta x)\] is a funcion of delta x.
\[Y_{0}=h(\Delta x)\] is also a function of delta x.
if \[pointO \rightarrow \lim_{\Delta x \rightarrow 0} (X_{0} , Y_{0})\]
then what is the significance of pointO?