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1. Runges function is written as f(x) = 1 25r2 (a) Develop a plot of this function for the interval from x =-1 to 1 using Ma
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Consider the Runges function as f(x)=1+25x2 The graph of the funon-25x The graph of the function f(x)- from the interval-1 tThe fourth order Lagrange interpolating polynomial using equispaced function values corresponding to x=-1,-0.5,0,0.5, l (x-x.The graph of the function f(x)-3.777866r-4.1362*+ from the interval-1 to 03 -0.5 0.5 y-3.77786 ґ-4.136.2 + 1 03 The Newton- DTable for the Newtons Divided Difference 10.0385 0.1988 1.5254 3.31587 3.31587 0.5 0.1379 1.7242 3.4484 3.31587 1.7242 1.525y 03 -0.5 0.5 y= 3.31587x -4.27737 x®十0.9973 -03 The value of the function at 0.s0.3820 The Cubic-Spline Method for the dataAnd the unknowns are finding by the equation For the natural spline f(x )-0 (-0.5 +1)/(%)+2(0+1) (x)-(0+0.5)/(%)= (1-0.1379Calculate the unknown from the equations use the matrix normal form then the value of the j(x)-9. 1524, f(x)--11.9294./(与)

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