make mathlab code (Numerical Integration) Suppose we are given a function f(x) whose integral is notknown explicitly. We may, however, wish to still approximate the value of the definiteintegral of f over the interval [a, b). In order to do this, we could use the so-calledcomposite trapezoid rule with n+1 nodes given byhn-1[S(2) dzx = (5(a) +2E f(a + kh) +,+2Ef(a + kh) + f(bk=1where h = b-acomp_trap_rule Function:Input variables:• an anonymous function representing f• a scalar representing the lower bound of integration a• a scalar representing the upper bound of integration b• a scalar representing the value of n; you may assune this is an integergreater than 0Output variables:• a scalar representing the approximate integral computed by the formulaaboveA possible sample case is:> int = comp_trap_rule(@(x) x^2, 0, 1, 100)int =0.33335

Answered: (Numerical Integration) Suppose we are…

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter5: Repetition Statements

Section5.7: Do While Loops

Problem 6E: (Numerical analysis) Here’s a challenging problem for those who know a little calculus. The...

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Explain the Wronskian determinant test. Using the Wronskian determinant test, write the program using NumPy to determine whether the functions f(x)=e^(- 3x), g(x)=cos2x and h(x)=sin2x are linearly independent in the range (-∞, + ∞). #UsePython
(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.
--Discrete Math Now, to work with some FSAs over the alphabet Σ = {a, b}. Give a regular expression and draw an FSA for the language of strings that have two “a”s. Give a regular expression and draw an FSA for the language of strings that have one “a” OR have more than one “a” and end with a “b”.
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4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..
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5. (a) Write a function that solves the general linear least-squares problem. The inputs to your function should be a vector of a values, a vector of measured y values, and an anonymous function that calculates a single row of the Z matrix. Inside your function, use the inputted anonymous function to create Z row-by-row, then use Z to create the normal equations. Solve these normal equations to obtain the computed coefficients that define the best-fit of your model. Your function should output these calculated coefficients. Again, include an error check that makes sure the input vectors are the same size. You may not use any built-in MATLAB functions to solve the normal equation. You can use any functions you have developed solves Ax = b via LU-decomposition is one option. e.g. a function you have that (b) Test your function in (a) to fit the following model to the given dataset (see belo y = a + bx (c) Test your function in (a) to fit the following model to the given dataset…
can you explain the solution in this problem, and especially how to get the f and k here?

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