The following data is given:  x 1 2.2 3.4 4.8 6 7 y 2 2.8 3 3.2 4 5 (a) Write the polynomial in Lagrange form that passes through the points; then use it to calculate the interpolated value of y at x = 5.4 .  (b) Write the polynomial in Newton's form that passes through the points; then use it to calculate the interpolated value of y at x = 5.4 .

Q: For the data given in the following table: 0.1 0.9 1.2 1.8 y 4.824 7.736 12.392 31.208 (A) Determine…

A: Let us take set of data points: x x0 x1 x2 x3 y f(x0) f(x1) f(x2) f(x3) Here x0, x1,…

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Q: 1. Given the data 1 2 5 7 8 f(x) 3 6 19 99 291 444 Calculate f(4) using Newton's Interpolating…

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Q: When calculating the first Lagrange polynomial using xo, X, we obtain L,(x) = x – 3, then Xo and x1…

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Q: (h) Write down the Lagrange's polynomial through (x0, fo), (x1, f1), (x2, f2). Hence express

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Q: Q.5: For the given data; x f(x) 1 3 2 6 3 19 5 99 7 291 8 444 Calculate f(4) and f (2.5) using third…

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Q: Given the data 2 5 6 f(x) 4 5.25 19.75 36 a) Calculate f (4) using Newton's interpolating…

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Q: Question 3 For the data given in the following table: 0.1 0.9 1.2 1.8 y 4.824 7.736 12.392 31.208…

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Q: 4. Given these data X 1 2 3 5 f(x) 3 19 99 Calculate f(4) using Lagrange polynomials of order 3. 7…

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Q: 2. (a) Using Lagrange Inverse Interpolation method, find the value of x when y= 29 for the following…

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Q: Find the newton polynomial formula for the given data 4 6 10 f(x) 1 3 8 16 Select one: 3x² – 22x +36…

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Q: The following data is given: 2.5 3 4 5 1 7 8 1 a) Write the polynomial in Lagrange form that passes…

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Q: Question 3 For the data given in the following table: 0.1 0.9 1.2 1.8 y 4.824 7.736 12.392 31.208…

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Q: 1. From the following data, perform the required fitting. i 1 2 4 6. 3 9 X 12 14 Y 15 21 27 36 42 a.…

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Q: [C] Obtain the interpolating polynomial of the form ax³ + bx² + cx + d (where a, b, c, d are…

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Q: 7. The following data is given: 3.4 3 2.2 4.8 2 2.8 3.2 4 5 (a) Write the polynomial in Lagrange…

A: Lagrange Interpolation formula f(x)=(x - x1) . . . (x - xn)(x0 - x1) . . . (x0 - xn)f0+(x - x0) . .…

Q: 3. The Lagrange polynomial that passes through the 3 data points is given by x| 15 | 18 | 22 y 24 37…

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Q: 1 2.2 3.4 4.8 7 2.8 3 3.2 4 5 Write the polynomial in Lagrange form that passes through the data…

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Q: Find a polynomial of degree two interpolating the three data points (0, 1), (a + 2, 5) and (B + 12,…

A: Note:- In this problem you don't mention about  α, β. So, i'm assuming them as constant. If it is…

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 1 3 5 7 2…

A: See the attachment.

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Q: 3. Given the following data: 0. 3. 4 6. f(x) 7 11 28 63 89 (a) Complete a Divided Difference Table…

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Q: 3 4 6. 0. f(x) 7 11 28 63 89 (a) Complete a Divided Difference Table for this data. (b) Construct a…

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Q: When calculating the first Lagrange polynomial using xo, X1 we obtain L,(x) = x – 3, then xo and x1…

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Q: When calculating the first Lagrange polynomial using x0, X1 we obtain L,(x) =x-3, then Xo and x, are…

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Q: z+1 (a) (z2-16)(z+2)

A: We have to identify the poles first.

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Q: Q5) Consider the Table below. y, = f(x,) 0.5 25.5 1 1.2 8.75 2.5 12.5 3 3.2 5.25 Find cubic Newton…

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Q: Q1/ From the following set of data: A) Calculate f (0.25), using Newton's divided difference formula…

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

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data y=f(x) 4 10…

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Q: 2. Consider the data: X 0.1 0.2 0.3 0.4 0.5 f(x) | 1.40 1.56 1.76 2.00 2.28 Use the Newton's forward…

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Q: if √0 =0, √T = 1 and √4 = 2 estimate √3 Compare by constructing Lagrange polynomial, ther with the…

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Q: Find the Lagrange and the Newton forms of the interpolating polynomial for these data: -2 0 1 f(x) 1…

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Q: Consider the following set of data: 8.3 8.6 8.7 y 17.56492 18.50515 18.82091 a) Write down the…

A: x x0 = 8.3 x1 = 8.6 x2 = 8.7 y == f(x) y0 = 17.56492 y1 = 18.50515 y2 = 18.82091

Q: for the function f (x) = x + . Estimate a) Lagrange interpolating polynomial b) Newton's…

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Q: 1. Find the Lagrange form of the interpolating polynomial for the following table of values: *| 1/3…

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Q: Q1. Given the data in the table below 1.6 2 2.5 14 3.2 4 4.5 f(x) 8 15 8 Calculate f(2.8) using…

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Q: 2. Given these data X 1 3 7 f(x) 3 19 99 291 Estimate using Newton's interpolating polynomial and…

A: x fx fxi, xi+1 fxi, xi+1,xi+2 fxi, xi+1,xi+2, xi+3 fxi, xi+1,xi+2, xi+3, xi+4 1 3             3…