6. Use the Newton's Interpolating Polynomial to determine y at x = 3.5 to the bestpossible accuracy. Compute the finite divided differences and order your points toattain optimal accuracy and convergence.Xy0215.43752.57.351637.56254.58.445359.1875612

x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12 Point of approximation x=3.5

Answered: 6. Use the Newton's Interpolating…

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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lim Sin (1-Gst) 1- Cast ·
2Use Newton's interpolating polynomial to determine y at *=8 to the best possible accuracy. Compute the finite divided differences as in Fig. 17.5, and order your points to attain op- timal accuracy and convergence. That is, the points should be centered around and as clase as possible to the unkiown. 01 2 5.5 y 0.5 16 11 3.134 5.3 9.9 10.2 9.35 7.2 6.2 13 18
In the graph below, a rectangle is inscribed in the first quadrant with its base on the x-axis and its upper right corner on the curve y = 2/7 – 2x . (x.y) 05 1.5 2 25 (a) Find the dimensions of such a rectangle with the greatest possible area. (b) Show that the dimensions you found produce a local maximum for the area using the first or the second derivative test. You do not need to argue that your answer is a global maximum. (c) What is the resulting maximum area? Enter the maximum area in the blank below. Round your answer to two decimal places.
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0. A particle moves along the x-axis. The velocity of the particle at time t is given by v(t) = 4 If the %3D t+1 position of the particle is x 1 when t = 2, what is the position of the particle when t = 4 ? (A) 0.617 (B) 0.647 (C) 1.353 (D) 5.713
(6) In class we showed that (1+ x)* ~ 1 + kx. (a) Using this formula estimate (1+.01)10, (1 + .1)1º, (1 + 1)10, and (1+ 2)10. How do these estimates compare to the actual values from your calculator? (b) Give a range of values of x for which our formula (1 +x)k = 1 + kx work. (c) Show, using (1+x)* × 1 + kx, that 1+ (1+ x)' + (1+ x)² + ... + (1+x)10 = 11 + 55x. Use this to estimate: 1+1.001 + 1.001² + 1.0013 + 1.0014 + ... + 1.00110.
Use Gauss forward formula
x = 1.25

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6. Use the Newton's Interpolating Polynomial to determine y at x = 3.5 to the best possible accuracy. Compute the finite divided differences and order your points to attain optimal accuracy and convergence. X y 0 2 1 5.4375 2.5 7.3516 3 7.5625 4.5 8.4453 5 9.1875 6 12