Let P(x) be the Lagrange interpolating polynomial that fits the data (–3,1); (-1, 3) and (4, 3). Then P(3) is O 25/7 3/2 O 25/9 29/8

Q: Use this interpolating polynomial for the data points f(x) 1 0-368 1-2 0-301 1-3 0-273 1.5 0-223 To…

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Q: Q1-Using the nodes (x, =2, x-=2.5 and x; =4), to find the second interpolation polynomial for flx) =

A: Given nodes are x0=2, x1=2.5, x2=4 and function is f(x)=1x Now table is x 2 2.5 4 f(x) 0.5 0.4…

Q: Determine the interpolating polynomial in Newton's form that passes through the points and Use the…

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Q: 2. Find the polynomial the passes through the following points (0,0), (2, —2), (4,0)

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Q: Let P(x) be the Lagrange interpolating polynomial that fits the data(-1,2); (4,2) and (7,5). Then…

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Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

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Q: Using pencil, paper and calculator, form the Lagrange interpolating polynomial corresponding to the…

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Q: Consider the data (1,10), (3,6)(1,10), (3,6). Then, Newton's polynomial that interpolates the data…

A: Solution of given problem is followed by Newton's interpolation formula.

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: Determine the linear interpolating polynomial that passes through the points (2,4) and (5,1). p(x) =…

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Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

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Q: Consider the data given below: x 0 2 3 f(x) 7 11 28 (i) Find the Lagrange interpolation and Newton…

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Q: Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2,…

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Q: Find y(5) if a second-degree polynomial is fitted to the data points (1, 4), (2, 6), (3, 9), (4,…

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Q: Let P(x) be the Lagrange interpolating polynomial that fits the data (-2,3); (2,4) and (4,3). Then…

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Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.

Q: (5) Use your graphing calculator to check your answers to (2) and (4) are correct. 7. (1.2 Ex45) (1)…

A: Hello. Since your question has multiple parts, we will solve the first parts for you. If you want…

Q: Find the interpolating polynomial p(t) = a0 + a1t + a2t2 for the data (1, 14), (2, 18), (3, 20).…

A: Answer

Q: For a data set {xi, yi ; i=1,n}, which of the following conditions must be satisfied by an…

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Q: Find y(5) if a second-degree polynomial is fitted to the data points (1, 4), (2, 6), (3, 9), (4,…

A: The given problem is to find the second degree polynomial and find the value of polynomial at x=5…

Q: Q// Fit a second-order polynomial to the following data: Y 9 8 3 7 9 11 9 6 1 7 1 3 10 9. 1 a. y =…

A: Given x y 9 8 0 3 7 9 11 9 6 1 0 0 0 7 1 3 8 10 9 1

Q: 3. Find both linear and quadratic interpolating polynomials for the points (-2,-13) , (-1,-3) ,…

A: We take given pairs of points as (x, y) x y -2 -13 -1 -3 1 -1 2 -9 3 17 We have…

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: If R₂(x) is the second degree Lagrange interpolating polynomial for the data Xi Yi where the…

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Q: A third degree polynomial passes through the points (0,-3),(,0),(2,9), (3,30), (4,69) and (5, 132),…

A: Using Newton's forward difference method:f(x) = f(x0) + (r)∆y + (r)r-12!∆2y +  (r)r-1(r-2)3!∆3y…

Q: Determine the Newton's Divided-Difference Interpolating Polynomial P,(x) written in Newton's…

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Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

A: We use Newton's Divided Difference interpolation formula. x      x0      x1      x2      x3y      y0…

Q: It is possible to write rk as a linear combination of Chebyshev's polynomials, for example Suppose…

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Q: 3. Let P3 (x) be the interpolating polynomial for the data (0, 3), (1, 4), (2, y), and (3, 0). The…

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Q: Find a polynomial interpolation to data (-1, 0), (0, 0), (1, 0), (2, 6) using Vandermonde method

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Q: Given (xi, x2024) Vi = 0,...,n, where x0 = -1, x₁ = 0, x2 = 1, x3 = 2, ..., xn = n = 1. Write down…

A: (a). When n=1, we have to points: (x0​,x02024​)=(−1,1) and (x1​,x12024​)=(0,0).  The interpolating…