Code this with C language.

Using Lagrange, Hermite, and Cubic Spline interpolation, interpolate the functions below with 13 data(points) that you can choose anyway under the range of x (-5<=x<=5). The output of the interpolation file must be txt file which contains enough x and y values of the function so that it is possible to draw the graph with the gnuplot in linux.

1) y = 1/(1+x^2) -5<=x<=5

2) y = 1 (when x>=0)

= 0 (when x<0) -5<=x<=5