a) Find the degree-2 interpolating polynomial via Newton's divided difference forf(x) = using nodes x = 0, x₁ = 1, and x₂ = 2.X1+xb) What are the degree-2 interpolating polynomials associated with Lagrange's con-struction and Neville's construction? Compare them to the solution of Part (a).

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Answered: a) Find the degree-2 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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solve only (a) part asap
(16) A triangle is inscribed in the unit circle in such a way as its base is the line segment along the x-axis from (-1,0) to (1,0), and its third point sits on the top half of the circle, somewhere in the first or second quadrant. Find the largest area this triangle could have.
Use Newton's method to find the zeros of f(x) = 4x² - 4x² using the given starting values in (a) through (c). (a) xo = -1.5 and Xo = - 0.9, lying in = O A. For Xo = B. For Xo -1.5 and Xo 1.5 and Xo √2 (-∞, -1/2) == - 0.9, Newton's method does not converge. The values of x; alternate between 1.5 and 0.9 as i increases. == -0.9, X₁→ as i gets large.
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5. (a) Rewrite t+ß using Euler's Formula. (b) Construct an example of a Cauchy-Euler equation whose characteristic equation has non- real roots. (c) Solve the equation you constructed in part (b) and use the formula from part (a) to rewrite the solution in terms of real valued functions.
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Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], what special case is this? Cauchy-Euler Equation B. Legendre Equation C. D. Variation of Parameters None of the choices
please explain full steps in detail and show steps Determine if g(x) = sin(x2) is uniformly continuous on R.
8) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √r can be approximated by iterating X¡ +1² (x₁+1=1) using an initial guess x₁. Because √ is the positive solution to the equation x² - r = 0, derive the iterating formula above by simplifying the Newton's method formula using f(x)=x²-r. Note that since r is a constant, d/dx(r) = 0. 9) Use the divide and average method derived in Exercise 8 and modify your code from Exercise 5 (three times) to calculate the square roots of the following numbers to within 8 decimal places (a) r = 2 (b) r = 3 (c) r = 5 You do not need to include all of the code for these problems in the HW you turn in, as most of it will just be the same as number 5. However, write down the first 5 to 8 lines (depending on the language used) that define the function used, the initial guess, and the tolerance, along with the roots found in the end.

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a) Find the degree-2 interpolating polynomial via Newton's divided difference for using nodes x = 0, x₁ = 1, and x₂ = 2. f(x) X 1+x b) What are the degree-2 interpolating polynomials associated with Lagrange's con- struction and Neville's construction? Compare them to the solution of Part (a).