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(Solved): *Exercise 2: *Use the divided difference method to approximate derivatives and do the following. Wri ...
*Exercise 2: *Use the divided difference method to approximate derivatives and do the following. Write the code in Python:
Recommended libraries to use: sympy, numpy, matplolib, and pandas
Create a theoretical framework that explains in detail what the method consists of.
? Create the pseudocode for a program that allows you to approximate the derivatives of any order of a real function.
? Create a flowchart for the program from the previous item.
Construct the program code for the previous two items in Python.
Use the above code to approximate the 1 st to 10 th order derivatives of the function f(x)=(xe^(-x^(2)))/(x^(2)+1) en x=0, taking the values h=0.5,
0.25,0.1,0.05,0.025,0.001,0.0005,0.00025,0.00005,0.000001. How sensitive is it when taking values closer and closer to 0 ? How
sensitive is the method when considering very large order derivatives?