( (1,0.2213)(1.7,0.9881)(1.9,-0.3442)(2.1,1.3875)(2.5,-0.9887) ) a) Find first order polynomial b) Find second order polynomial 2) With the user-friendly program developed on the course site to obtain the first derivative estimates for unequally spaced data. If the function is [ y=x^{2}+5 x e^{x} ext { at } x=3 ext { using step size of } h=0.006 ] a) Forward difference approximations of ( O(h) ) : b) Bacward difference approximations of ( O(h) ) : c) Central difference approximations of ( Oleft(h^{2} ight) ) : d) Central difference approximations of ( Oleft(h^{4} ight) ) : 3) Integrate the fowloing function by using the data given below: [ egin{array}{c} f(x)=left(7-12 x^{3} ight)^{4}+x sin (3 x)-2 x cot (sqrt{x}) \ a=0.2, b=0.5 ext { and } M=7 end{array} ] A. Trapezoidal rule : B. Simpson's rule :

Open courses-Math252-Achives-Lab-Least Square.rar 1) Use the Least squares method to find the polynomials below; (1.0.2213) (1.7, 0.9881) (1.9. -0.3442) (2.1, 1.3875) (2.5, -0.9887) a) Find first order polynomial b) Find second order polynomial 2) With the user-friendly program developed on the course site to obtain the first derivative estimates for unequally spaced data. If the function is y= x+5xe at x = 3 using step size of h = 0.006 a) Forward difference approximations of O(h): b) Bacward difference approximations of O(h): c) Central difference approximations of O(h): d) Central difference approximations of O(h): 3) Integrate the fowloing function by using the data given below: f(x) = (7-12x)*+ xsin (3x) - 2x cot () a=0.2,b=0.5 and M = 7 A. Trapezoidal rule: B. Simpson's rule: