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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 dierence
2. 2-point backward dierence
3. 3-point central dierence
4. 5-point central dierence
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 dierent methods for values of n=10, 100, 1000, 10000. Plot the dierent 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.
Submit solutions for all of the following questions. Remember to set out your answers showing all steps completely and explicitly justify your steps. 1. Provide, in no more than
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d^2y/dx^2 if x=ct,y=c/t
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6 412.56356
ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories Examp
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