DETERMINE THE VALUE OF F(5) FOR A GIVEN SET OF DATA BELOW USING THE STATED METHOD OFINTEPROLATION:XF(x)7-2011322-15410A. LAGRANGE POLYNOMIAL INTERPOLATIONB. QUADRATIC INTERPOLATION

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Answered: DETERMINE THE VALUE OF F(5) FOR A GIVEN…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For the following polynomial: f(x) = (x – 1)2 ( x2– x – 30) 3a) Describe the end behavior of the graph. (You 3b) Find the x and y-intercepts 3c) Is the graph of this function both smooth and continuous? Explain why or why not? 3d) Provide a sketch of the function. How did you use your answers to parts (a), (b), and (c) to sketch the graph.
A(x) is a quoadratic function. B(x) is a quadratic function. What type of polynomial function is A(x) ·B(x)? 1. 2. A(x) is a linear function. B(x) is a linear function. What type of polynomial function is A(x) · B(x)?
Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3 using node points x; = i, i = -1,0, 1,2 : f(x) = 3x² – e*
Assume the polynomial P5(x) interpolates a function f(x) at the six data points (xi, f(xi)) with x-coordinates ₁ = 0.0, 2 0.0, x2 = 0.2, x3 = 0.4, x4 = 0.6, x5 = 0.8, x6 = 1.0. Assume that the interpolation error at x = 0.3 is |f(0.3) - P5(0.3)| = 0.01. Estimate the new interpolation error |ƒ(0.3) — P7(0.3)| that would result if two additional interpolation points - (x7, y7) = (0.1, f(0.1)) and (x8, ys) = (0.5, f(0.5)) are added. What assumptions have you made to produce this estimate?
(a) Consider the table below for an arbitrary function y = f(x). 1| 2 3 4| 5 6 7| 8 f(x) 9 37 243 1017 3109 7749 | 16767 32713 58977 i. Draw a forward difference table for above table. Use your table to give the numerical values for: ii. Af2 iii. A²fa iv. Aºfi v. What is the degree of the polynomial from which these values were obtained from? (b) Find the specified higher order forward differences specified with the given en- tries: i. A°yo given that yo = 20, yı = 50, y2 = 90, y3 = 100, y4 = 150, y5 250. 200, y6 ii. A'yo given that yo = 79, yı 218, y6 = 250, y7 = 300. iii. A*y given that yo = 120, y2 150, уз 190, Ул 201, y5 160, y1 400, y6 = 410, y7 = 460, ys = 500. 200, y2 240, y3 = 300, Y4 = 350, y5
7. The function shown is a second-order piecewise polynomial, plot the function yourself: 22 y 20 18 16 14 12 10 8 6 0 1 2 3 4 X 10 5 6 7 8
Use Algorithm 3.2 (Divided Difference) to construct the interpolating polynomial of degree three for the following data: f(1) = 1.2,f(2)= 1.6,f(4)=2, and f(5)=2.6 , then f(2.6)

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DETERMINE THE VALUE OF F(5) FOR A GIVEN SET OF DATA BELOW USING THE STATED METHOD OF INTEPROLATION: X F(x) 7 -20 11 32 2 -15 4 10 A. LAGRANGE POLYNOMIAL INTERPOLATION B. QUADRATIC INTERPOLATION