Suppose that Pɔ(x) is the second degree Lagrange interpolating polynomial for the data: 1 2 Yi 3 6 18 Xi 4 Then f(3) ~ P2(3), which is closest to

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: Use the given data, for some function y, to construct the Lagrange interpolating polynomial of the…

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Q: 2.1 Find the appropriate Lagrange interpolating polynomial using the following data table 2 0 0.5 1…

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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: (a) Table 1 shows the COVID-19 data in Malaysia. Compute using Lagrange Interpolating Polynomial: i.…

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

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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: 2.1 Find the appropriate Lagrange interpolating polynomial using the following data table 0 0.5 1…

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Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

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Q: Construct the Lagrange Interpolation polynomial for the fundlion y= Sinin taking the points. 6.

A: Given  y=sin(πx)x0=0,x1=1/6,x2=1/2

Q: Consider the following table: Xi 5 6 f(X) 7 12 14 Find f(4) using Lagrange method for interpolation.…

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Q: X 1 2 3 4 f(x) 2,6 3,5 3,2 2,4

A: From the given table, The general formula is,

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

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Q: The Lagrange polynomial that passes through the four data points is given by x 15 18 22 30 y 24 37…

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Q: Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced…

A: In the question it is asked to construct interpolating polynomial using the table given in question.

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

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Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

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Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: Construct the Lagrange interpolation Polynomial for the function Y= Sin Tx, the ponts =0, 2, =…

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Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: Let ro = -a; xi = 0; and x2 = a. Compute the interpolation polynomial for f(x) = -r* using Lagrange…

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Q: For the given polynomial y = azx2 + azx³, determine az and az that will make (1, 3) a point of…

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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: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

A: Given: x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12 To find: Construct the…

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: 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: Determine the linear Lagrange interpolating polynomial that passes through the points (2, 4) and (5,…

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Q: (a) Develop a table of f(x)=2e* + 3x for x = 3, 5, 7 and 9. (b) Estimate f(4.2) using the…

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Q: I Example 6.10. Assuming that the following values of y belong to a polynomial of degree 4, compute…

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Q: Use the numbers x, = 2 , x, = 3 and x, = 4 to find the second Lagrange interpolating %3D polynomial…

A: First of all we have to find the second Lagrange interpolating polynomial for f(x)=1/x Then we have…

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

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Q: The following table shows the lifting force on an aircraft wing measured in a wind tunnel at various…

A: let the polynomial of degree 5 be                                                  Lifting…

Q: Let f(x)=x*-2x. Use cubic Lagrange Interpolation based on the nodes Xo =-1,X1=0,x2= 3,X3=4 to…

A: Given, fx=x4-2x3 x0=-1, x1=0, x2=3, x3=4 To approximate the value of f3.5.

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: Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5 , x, =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: The Lagrange polynomial that passes through the four data points is given by 15 18 22 30 y 24 37 25…

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Q: Approximate f' (2) using the given data f(0) = 1, f(1) = 2, f(2) = 4, and f(3) = 7 and the Lagrange…

A: Given data points are: x x0 =0 x1 =1 x2 =2 x3 =3 f(x) 1 2 4 7 Lagrange interpolation…

Q: · Construct the Lagrange interpolation polynomial for the data 1 2 -1 f(x) 1 1 5 -1 Hence,…

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Q: Compute the interpolating polynomial through the points (–1, 5), (1, –3), (3, 21) using the…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5, X2 =4…

A: Find second order Lagrange interpolation polynomial

Q: Let P(x) be the Lagrange interpolating polynomial of f(x) = 2x2 +3 at the points xo = 0; x1 = 1 and…

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Q: Use appropriate Lagrange interpolating polynomial for the following table and approximate f(1.5) Xi…

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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) Table 1 shows the COVID-19 data in Malaysia. Compute using Lagrange Interpolating Polynomial: i.…

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Q: 4. Let P,(x) be the Lagrange interpolating polynomial for the data (0,0), (0.5, y), (1, 3) and (2,…

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Q: QCx) = (x +s)? (x=3)4 %3D

A: Q(x)=(x+5)2(x-3)4

Q: Find the linear interpolation Lagrange polynomial P1(x) using the following data: (Xo.Yo) = (0, -1)…

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