1. What is the definition of the “machine precision” in the context of the IEEE double-precisionfloating point format?
2. Let f : R→R be a three-times continuously differentiable function. Consider the numerical difference formula
with real-valued coefficients a,b ∈ R. For which values of a and b is the mathematical approximation error of order O(h2), i.e., such that
) ?
3. Plot the numerical evaluation error of the above finite difference formula for and f(x) = sin(x) at x = 0 and at x = 1 using a logarithmic scale on both axis and interpret your results. For which values of h would you recommend using this formula? You can use any programming languange of your choice to complete this exercise.
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