Use the given data, for some function y, to construct the Lagrange interpolating polynomial of the data 2 3 1. 3. Yi 1 2 7 20 Accurate to two decimal places (using a decimal point and not a comma), estimate

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,…

Q: Given the following table of data, X 6.6 6.8 7.0 7.2 7.4 f(x) 8.820 18.501 28.423 38.102 47.021 find…

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Q: 2. Given these data | 1 | 3 6 DA 19 | 7 f(x) 3 99 291 Estimate using Newton's interpolating…

A: Newton's divided difference interpolation formula is:…

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3 5. y=f(x)…

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Q: Find the Newton's polynomial which interpolating the following data. 1 2 3 4 5 f(x) 3.6 1.8 1.2 0.9…

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Q: The following data define the sea-level concentration of dissolved oxygen for fresh water as a…

A: (a) Find the Newton's forward difference table.

Q: With the given data points below, use every method in Polynomial Approximation and Interpolation to…

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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…

A: Let the given data be x0,y0, x1,y1, ..., xn,yn. To obtain the n-th order Lagrange interpolating…

Q: Given the following data which generated by the function y = 1/x. %3D X 1 2 4 5 y=f(x) 1 0.5 0.3333…

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Q: Obtain the Lagrange interpolating polynomial using all the data points below: 0.5 1.0 1.5 2.0 2.5…

A: Introduction: The Lagrange interpolating polynomial is a basic interpolating polynomial that fits…

Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

A: Solution : y=f(x) 1. Lagrange's Interpolation formula is,…

Q: Find Lagrange interpolation polynomial P(x) which agrees with the following data and obtain a 1…

A: The Lagrange's interpolation polynomial for a function, y=f(x) that passes through the points x0,y0…

Q: 9) Find the cost of estimating f(x) using Lagrange interpolating polynomial p2 (x) for a specific…

A: To find: Cost of estimating fx¯ using Lagrange interpolating polynomial P2x for a point x¯. We shall…

Q: From a function, f(x), we obtain the following data points: (ri, f(x₂)) = {(-0.5, e³/2), (0, 1),…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3 7. y=f(x)…

A: If y=fx takes the values y0,y1,....,yn corresponding to x0,x1,....,xn then the Lagrange's…

Q: Let P(x) be the Lagrange interpolating polynomial of f(x)%3= 3x +3 at the points Xg 0: x 1 and x; =…

A: 1/15 is the answer.

Q: The following data shows the height function of a hill a a distance x from a reference. Form a cubic…

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Q: We are given the following data for the velocity as a function of time: 10 227.04 362.78 517.35…

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Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

A: The given data is f(0)=2 ,f(1)=3, f(2)=12, f(3)=41.

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.…

A: a. Tabulate the given value as follows, x y 3 9 5 15 7 21 9 27 12 36 14 42

Q: Using the provided data, find the interpolated value of f(x) when x = 3 using Newton's Divided…

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Q: According to the Table below calculate the function value at x = 2: a) by using Linear Interpolation…

A: The given table of values is

Q: 1. Use the data given below to estimate f(3) by X 1 4 f(x) 62 Constructing: a. Linear polynomial b.…

A: Please find attachment below

Q: Let P(x) be the Lagrange interpolating polynomial of 1 f(x) = at the points xo = 0; x, = 1 and x =…

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Q: The following data of the velocity of a body is given as a function of time Time (s) 0. 15 18 22 24…

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Q: 2. Consider the following data values 1.5 2 2.5 3 f(x) 8 14 18 Find the value Of f(x) at x= 2.65…

A: Newton's divided difference interpolation formula is a interpolation technique used when the…

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.

Q: Interpolate the following data to estimate the pressure at 6 minutes using 2nd order polynomial (By…

A: Lagrange's interpolation formula for the second-order polynomial is . The points for the polynomial…

Q: Given the data: 2.1 2 1.4 2.7 3.4 3.2 y 12 8. 2 5. 10 17 Determine y at x= 2.5 using: a) Newton's…

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Q: Let P(x) = 2x³ + x² + 1 be the Lagrange interpolating polynomial that approximates a function f over…

A: The given problem is to approximate the integral of the function f(x) over the given interval with…

Q: Obtain the Lagrange interpolating polynomial using all the data points below: x 0.5 1.0 1.5 2.0 2.5…

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Q: Consider the data below: X 200 240 300 350 f(x) 1100 980 820 700 Approximate f(320) using Lagrange…

A: Given: The value of table for x and y x 200 240 300 350 y 1100 980 820 700 The objective is…

Q: The following data define the sea-level concentration of dissolved oxygen for fresh water as a…

A:

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(5) = 147 and the…

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Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

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Q: Let P(x) be the Lagrange interpolating polynomial of f(x) = x³ – 3x + 3 at the points x, = 0; x, = 1…

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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…

A: Given,

Q: Interpolate the following data to estimate the pressure at 1.5 minutes using 2nd order polynomial…

A: The order polynomial approximation of f(x) using Lagrange Interpolation is  .

Q: 3. For the following data set, find the interpolating polynomial by the Lagrange's Method. 2. 4.

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Q: By using Lagrange's interpolation polynomial of order 1 through 3. Calculate f(3.5) from the…

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Q: Given the following table of values, use Lagrange Interpolation to find the 2nd degree polynomial of…

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Q: Given these data X 1 2 7 f(x) 3 19 99 291 Estimate f(2.5) and f(4), (a) using an interpolating…

A: NOTE: According to guideline answer of first method can be given, for other please ask in a…

Q: Construct the Lagrange interpolating polynomial of degree 3 for the following data. And calculate…

A: The polynomial for the data can be calculated using Lagrange's interpolation. The formula for…

Q: Interpolate the following data to estimate the pressure at 7 minutes using 2nd order polynomial (By…

A: Given,

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: Q3. Use Lagrange interpolating polynomials of order а) 1 b) 2 c) 3 to determine y at x=1.32 for the…

A: Let  x0=1.20x1=1.25x2=1.30x3=1.35fx0=0.1823fx1=0.2231fx2=0.2624fx3=0.3001 The, Lagrange…

Q: 4. The upward velocity of a rocket is given as a function of time in Table 3. Table 3 Velocity as a…

A: The Lagrangian polynomial interpolation is given by,…

Q: The following data shows the height function of a hill a a distance x from a reference. Form a cubic…

A: Given Information: Consider the given data: x h 0 4 1 5 2 10 3 17 4 21 5 16 6 11…