The Lagrange polynomial that passes through the four data points is given by x 15 18 22 30 y 24 37 25 20 of The value of L3 at x=24 is: tion Select one: O 0.125 O0.750 O 0.075 O 1.446 O None O 0.228

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: 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 second Lagrange interpolation polynomial that fn tercepts f(x)= x2+xe*+sînx at points xo=0,…

A: NOTE: A, B and C are not subparts, they are options and we have to choose the correct one.  We have…

Q: Find the quadratic Lagrange polynomial for the data in the table below, and use it to compute…

A: Given table: x 0 1 2 fx 0 1 8 The objective is to find the quadratic polynomial and then to…

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: 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: 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: Find the Taylor polynomial T2(x) and compute the error |f(x) – T2(x)| for the given values of a and…

A: Given : f(x) = esin(x)

Q: Given the following data 2 3 y 1 11 a) Construct a maximum order of Lagrange polynomial…

A: The Lagrange's polynomial to approximate a function with 3 points, x0,y0 , x1.y1 , x2,y2 can be…

Q: Q3) Find the Lagrange polynomial that fits the followin value of y at x-0: Ans. y-6.03888 -2 3. 5.…

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Q: Approximate f(3) using an interpolating polynomial of degree 3 using Newton forward-difference…

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Q: Find the Taylor polynomial T;(x) and compute the error |S(x) – T2(x)| for the given values of a and…

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Q: The Lagrange polynomial that passes through the 3 data points (Xo,Vo) = (15,24), (x 1,V1) = (18,37),…

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Q: Let g(x)= Vx . Form a Lagrange interpolating polynomial of degree two to approximate the value of…

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Q: Let P(x) = 3x4 - 2x³ be the Lagrange interpolating polynomial that approximates a function f over…

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Q: True or False: If T E L(C³) and (T – 21)(T – 31)(T – 41) = 0, then the charac- teristic polynomial…

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Q: Suppose the following S shape of the total cost curve can be captured by the following cubic or…

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Q: Find T3 (x) (the Taylor polynomial of degree 3) for the function f at the number c. (a) f(x) 1 c= 2…

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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: Q2: Construct the second order Lagrange interpolation polynomial for the function f(x) = In(x + 1)…

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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: 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: 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: 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: 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: Q3) Find the Lagrange polynomial that fits the following set of four poin value of y at x-0: Ans.…

A: Given: - The set of four points, x -2 3 1 7 y 5 7 11 34 To find: - The Lagrange polynomial…

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: 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: Compute the Taylor polynomial T5(x) and use the Error Bound to find the maximum possible size of the…

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…By…

Q: Approximate f(0.5) employing Lagrange interpolation polynomial with the nodes Xo=0, X1=0.6, x2=0.9…

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

A: Lagrange's polynomial can be used to obtain the interpolation for the data. The polynomial is…

Q: To approximate f'(xo), suppose first that ro e (a, b), where fe C (a, b), and that x1 = xo + h for…

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Q: Q2: Construct the second order Lagrange interpolation polynomial for the function f (x) = In(x + 1)…

A: To find- Construct the second order Lagrange interpolating polynomial for the function fx = lnx + 1…

Q: 5) Find the velocity of rocket by using Gregory-Newton interpolation polynomial at t=260 sec. time…

A: Consider the given table. We have to find the velocityt=260 sec Since, t=260 sec is near to the…

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: Approximate f(0.5) employing Lagrange interpolation polynomial with the nodes xo=0, x1=0.6, x2=0.9…

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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: Q2 Given the data 5 f(x) 4.5 5.6 18.7 34 a) Calculate f (4) using Newton's interpolating…

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

A: Let  f(x)=x We have x f(x)=x 0 0 1 1 4 2 we have x0=0, x1=1, x2=4 Lagrange's polynomial…

Q: Q3: Construct a 3rd order Lagrange polynomial of the function f(x) = lnx.cosx where x e [1, 4]. Then…

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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: 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: The Lagrange polynomial that passes through the 3 data is given by 15 18 22 y 24 37 25 2 (x) = 24L1…

A: The three point interpolation formula through the points x0, y0, x1, y1, x2, y2 can be defined as…

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: Consider the function f(x) = , TE [0, 2]. Construct the Lagrange interpolation polynomial which…

A: Numerical methods: Legranges interpolation of the given data points

Q: Q.3: Determine the Lagrange interpolating polynomial by using second order form for the given data…

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Q: Let T3 be the Maclaurin polynomial of f (x) = ex . Use the error bound to find the maximum possible…

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