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

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Old   December 1, 2008, 04:49
Default Maximum of disturbance for function of y=rctan(x)
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Dear Friends:

The function: y=arctan(x),



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.



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Old   December 6, 2008, 20:09
Default Re: Maximum of disturbance for function of y=rctan
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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).
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