Maximum of disturbance for function of y=rctan(x)
 

Dear Friends:

The function: y=arctan(x),

x=0~infinite,

y=0~pai/2.

When x is subjected a disturbance, y has a corresponding disturbance. There may be a maximum (limit) of disturbance of y for a given value of y.

For example, at y=80 degree, maybe the maximum possible disturbance is 0.2 degree. Is it possible?

We want to find the maximum of disturbance of y in the whole range of 0~pai/2, i.e., to obtain the "maximum of disturbance of y" versus y.

It is appreciated if anyone can help.

Thanks

LargeBILL

Re: Maximum of disturbance for function of y=rctan
 

If a function is to be limited to a certain range, and you want to find what inputs to the function keep the output in the certain range, just use the inverse function.

I.e. if y=80+0.2, then calculate x_high = y^-1(80.2) and x_low = y^-1(79.8).