Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 6. X 0.4 0.8 1.2 1.6 y 00.25 1 2.25 4 6.25

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: Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute…

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Q: Interpolate the following data to estimate the pressure at 1.15 minutes using 2nd order polynomial…

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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…

A: Given data:   0 1 2 x -2 2 4 y 3 4 3

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

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 6. The following data are given for a polynomial P(x) of unknown degree. 0 12 3 P(x) 4 9 15 18…

A: Given all the fourth order difference are equal to 1 We have to find the coefficient of x3 Now make…

Q: Let P(x) be the Lagrange interpolating polynomial that fits the data (–3,1); (-1, 3) and (4, 3).…

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Q: Using the data of the table below, apply Gregory-Newton's backward divided differences to…

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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: If the Newton's Divided Difference second order polynomial for the coresponding x, y data is…

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Q: Complete the divided difference table for the data used in the following Table and construct the…

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Q: Fit a second-order polynomial to the data in the kollowing daha- 0|12/31415 yi 2.17.713.6|272 40.9…

A: The objective is to find a second order polynomial and to find the standard error.

Q: A bullet is fired upward with its velocity against time given in the table below: Time t in seconds…

A: The given problem is to find the value of velocity of time t=16 from the given data using Lagrange…

Q: X 3 4 F(x) 0.5 0.3333 0.25

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Q: Consider the tabulated data and suppose that (Oo(r) is the interpolating polynomial obtained by…

A: Take a quadratic polynomial as the interpolating polynomial. Apply the interpolation properties to…

Q: Change the following data, such that the data follows a certain fourth-degree polynomial. X: -2 -1 0…

A: Newton's divided difference formula can be defined as:…

Q: Approximate f' (2) using the given data f(0) = -8, f(1) = -7, f(2) = 0, and f(3) = 19 and the…

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Q: Q1 Table below contains dataset of a robotic arm during a force measurement on a thigh phantom.…

A: given data  Time(s) 10.5 13.1 15.2 Force(N) 9.27 11.90 13.83 (A) lagrange interpolating…

Q: 2. If m < n, show that mPa(x)dr deduce that r* P6(r)dr = 0. = 0, where Pn(x) denotes the Legendre…

A: We have prove the given problem.

Q: Q5. Use Newton's interpolatory divided- difference formula to construct interpolatin polynomial of…

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Q: Let P(x) be the interpolating polynomial for the data (0, 1), (1,3), (4, -3). Then P(2) = 3 4 -3 1

A: Here are 2 ways to solve find the solution In 2 method we will use this lagrange interpolation…

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: If the Newton's Divided Difference second order polynomial for the coresponding x, y data is…

A: Suppose a second degree polynomial passes through three data points  . x x0 x1 x2 y=f(x) fx0…

Q: Q3 Consider the following tabulated data for the vapor pressure P (mm Hg) of water as a function of…

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

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Q: 5. Is the following set of polynomials linearly independent in P3? Explain your work. 1+ 2t³, 2 +t –…

A: As per our guidelines we are supposed to answer only first question. Please repost other question…

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: Find the Hermite interpolation polynomial H(x) for the following data.

A: Given, the data

Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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Q: Let P(x) be the Lagrange interpolating polynomial that fits the data (1,2): (4, 3) and (7, 3). Then…

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

A: Given: some given data's are missing  The given data T°C 8 16 24 32 40 O,mg/L 14.621 11.843…

Q: 2.Use the Newton interpolation polynomial to find f(0.05) based on the following data points {(-0,5,…

A: Given data is  {(-0.5,0.97939),(0.15,4.72743),(0.5,13.69506),(1,61.25661)} we have to find the value…

Q: 2.0 Fit a cubic polynomial to the following data: 3 5 8 2.2 4 12 y 1.6 3.6 4.4 3.4 2.8 3.8 4.6

A: x y 3 1.6 4 3.6 5 4.4 7 3.4 8 2.2 9 2.8 11 3.8 12 4.6 cubic polynomial is of the…

Q: 2.3. Approximate fl1895) vising an interpolacting polynomial of degree & using Netu tons.…

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

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Q: The following x-y data is given 10 13 15 y 50 | 113 | 165 The Newton's divided difference second…

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Q: Fit a second order polynomial jo the following data 1 2. 3\ 4. 6. 01 0.5 1.0 1.5 2.0 2.5 0.25 1.0…

A: general second order polynomial equation :

Q: Consider the following data (xy): (-2, 1), (0, 3), (2, -1). Find the interpolation polynomials P(x)…

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Q: Q// Fit a second-order polynomial to the :following data Y 7 11 7 5 2 10 4 7 2 11 11 3 y = 8.440138…

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Q: The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in the…

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Q: Which of the following third degree interpolation polynomials can be developed from the given data…

A: Given x 0 2 4 6 y 2 4 14 40

Q: Fit a second order polynomial to the following data 1 2 4 0.5 1.0 1.5 2.0 2.5 0.25 1.0 2.25 4.0 6.25

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Q: Q8: Consider the following data 2.1 1 7.7 2 13.6 3 27.2 4 40.9 6 80.3 a. What is the degree of the…

A: Consider the given table. xi yj 0 2.1 1 7.7 2 13.6 3 27.2 4 40.9 6 80.3

Q: Consider the following data (xYk): (-2,0), (1,– 1), (3, -2). Find the interpolation polynomial P(x)…

A: Given x0=-2 , y0=0         x1=1 ,      y1=-1        x2=3 ,      y2=-2The interploting polynomial…

Q: Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute…

A: The given table is  x 8 9 9.5 11 f(x) 2.07944 2.19722 2.25129 2.39789 The objective is to…

Q: Find the following 2nd order interpolation polynomials for the given points (0, 1), (2, 5) and (4,…

A: Introduction: In numerical analysis, interpolation is very significant. It describes the function…