Let us take the arc of a curve and a fixed point P on it . Now take a variable point Q on the curve and let Q--->P. Then it is definitely ;
Length of arc as a function :-
Let y=f(x) be the equation of a curve on which we take a fixed point A .
To any given value of x corresponds a value of
y, viz.,f(x) ;
To that pair of numbers x and f(x) corresponds a point P on the curve, and this point P has some arcual length s from A.
Thus "s" is a function of x for the curve
Similarrly , we can see that "s" is a function of parameter "t" for the curve
and in function of theta for the curve