In this paper, a class of slightly perturbed equations of the form    x will be treated graphically and symbolically, whereis an analytic function of x. For graphical developments, we set up a simple graphical method for the real roots of the equation

In this paper, a reliable computational tool will be developed for the determination of the parameters of the stellar density function in a region of the sky with complete error controlled estimates. Of these error estimates are, the variance of the fit, the variance of the least squares solutions vector, the average square distance between the exact and the least-squares solutions, finally the variance of the density stellar function due to the variance of the least squares solutions vector. Moreover, all these estimates are given in closed analytical forms.