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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.
Fundamental Theorem of Calculus, Part I As noted through the title above it is only the first part to the Fundamental Theorem of Calculus. The first part of this theorem us
For the given function recognize the intervals where the function is increasing and decreasing and the intervals where the function is concave up & concave down. Utilizes this info
5.6:4=x:140
Example : Determine the Taylor series for f(x) = e x about x=0. Solution It is probably one of the easiest functions to get the Taylor series for. We just require recallin
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