Find the Lagrange form of interpolating polynomial p2(x) that interpolates thefunction f(x) =e-X² at the nodes x0 = 1, x1 = 0 and x2 =1. Further, find the valueof p2(-0.9) (use 6-digit rounding). Compare the value with the true value f(-0.9)(use 6-digit rounding). Find the percentage error in this calculation.

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Answered: Find the Lagrange form of interpolating…

Programming Logic & Design Comprehensive

9th Edition

ISBN:9781337669405

Author:FARRELL

Publisher:FARRELL

Chapter4: Making Decisions

Section: Chapter Questions

Problem 9RQ

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(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.
(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.
(Practice) Determine names for functions that do the following: a. Find the average of a set of numbers. b. Find the area of a rectangle. c. Find the minimum value in a set of numbers. d. Find the density of a steel door. e. Sort a set of numbers from lowest to highest

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