I as studying for math and I as studying the equation |x| and I as thinking in a way to draw that function in my calculator but I didn't know how to represent |x| so I got the idea of plotting sqrt(x^2) and it worked. Later I as confronted with a function like: -1 for -1 < x < 0 and 1 for 0 < x < 1 and because |x|' its that function I derivate the function sqrt(x^2) and obtained x/sqrt(x^2) and it worked its exactly the same except that the function is not defined in x = 0.
Is this "property" used, in my opinion I think it would be very useful for example in "heaviside" functions? Am I being stupid?
Example:
5 + 3 * heaveside(x-2) = 5 + 3 * ((x/sqrt(x^2) + 1)/2)
Is this "property" used, in my opinion I think it would be very useful for example in "heaviside" functions? Am I being stupid?
Example:
5 + 3 * heaveside(x-2) = 5 + 3 * ((x/sqrt(x^2) + 1)/2)