Suggest the piecewise constant interpolation of the function f(x)=sin(x), 0 <= x <= 381, at points x_i = ih, where h = 0.1. Thus, our interpolant satisfies v(x) = sin(ih), (i-0.5)h <= x < (i+0.5)h, for (i = 0, 1, ..., 3810).
Exercises:
a) Find a bound for the error in this interpolation.
b) How many leading digits in v(x) are guaranteed to agree with those of f(x), for any 0<=x<=381?