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Write an octave program that will take a set of points {xk, fk} representing a function and compute the derivative at the same points xk using
1. 2-point forward di erence
2. 2-point backward di erence
3. 3-point central di erence
4. 5-point central di erence
Use your program for the function
f(x) = ex
for which you know the correct answer to study the result as a function of h in the interval x ∈ [0; 1]. Make a table showing the values of the maximum absolute and relative errors for the 4 di erent methods for values of n=10, 100, 1000, 10000. Plot the di erent estimates for the derivative together with the analytical answer for 2 values of n. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.
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WHICH LIFE PROBLEMS CAN BE SOLVED USING THE KNOWLEDGE OF DIFFERNTIAL EQUATIONS?
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