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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.
Consider the trigonometric function f(t) = -3 + 4 cos(Π/ 3 (t - 3/2 )). (a) What is the amplitude of f (t)? (b) What is the period of f(t)? (c) What are the maximum and mi
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With reference to Fig. 1(a) show that the magnification of an object is given by M=SID/SOD. With reference to Fig. 1(b) show that the size of the penumbra (blur) f is given by f
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compare: 643,251: 633,512: 633,893. The answer is 633,512.
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