1. Create a program that computes the derivative of a given (either an algorithm for computing the function or a set of discrete data points (x, Yi), i = 0, 1, ..., n) function y = f(x) at the point x = Xk using any of the following methods: • First Central Difference Approximations • Second Noncentral Finite Difference Approximations • Richardson Extrapolation

Q: 5. Find the least integer n such that f(x) is 0(x") for each of these functions 5.a f(x) = 2x² + x³…

A:

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A: See the solution below-

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A: Solution:   Given,     f(0) = 0 f(1)  = 1

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Q: 1. In this problem consider the bisection method. (a) Write a PYTHON function computing an…

A: Note: Both subparts(a and b) solutions are indicated in the given code as a comment line.…

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Q: 4. An antiderivative of a function f is given by 3 [ f(x) dx = (4x²+x-3)√x+1 28 (a) Compute fi f(x)…

A: Start.Import the sympy module as sp.Define the symbol 'x' using sp.Symbol().Define the function 'f'…

Q: (Numerical Differentiation) Suppose we are given a function f(x) whose drivative is not known…

A: % matlab function to approximate the derivatiove of a function f(x) at point x = a, and stepside h…