1. (20 points) Find the polynomial of least degree that interpolates the data 3 7 1 2 X f(x) 10 146 2 1 in (a) Lagrange form (b) Newton form

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

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Q: 1. -1 0 1 2 f(Xx)| -4|-1 2 11 Table is given. a. Lagrange interpolation polynomial of degree 3. b.…

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Q: when x = 3.57 using quadratic Approximate y Lagrange Interpolating polynomial up to 3rd degree. Use…

A: Given table is xi yi 3.1 20.1810 3.2 22.5280 3.3 25.0470 3.4 27.7440 3.5 30.6250 3.6…

Q: 2. Find lagrange's Inerpolating polynomial of degree 2 approximating the function y = In x defined…

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Q: Exercise no.4 1. Use Lagrange polynomial estimate f(2) for the given data. x -2 -1 0 4 f(x) -2 4 1 8…

A: Given problem is to estimate the value f(2) using Lagrange polynomial and find the best fit curve of…

Q: A. Find the interpolating polynomial of the following point and function using Newton's…

A: Dear student, u posted many questions under one question...pls post one question from next…

Q: Determine Newton's Finite Divided Difference interpolating polynomial for the function values…

A: we are given  x f(x) 1 4 2 7 3 6 0 -15   (a)Newton's divided difference table  x…

Q: The Lo(x) of second degree Lagrange's polynomial is (x– xo)(x – xq) (x– xq)(x– x2) None of these (x–…

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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: (a) Find the equation of the following curve Ax) using Newton's divided difference polynomial.…

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Q: tion 10 Jsing Newton's backward difference polynomial of degree 2, for the below data, approximation…

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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: 4. a) Find the second Taylor's polynomial P2(x) approximating the function f (x) = e2* + cosx about…

A: Given function is fx=e2x+cosx.

Q: 3 Given f(x) = Vx+ 5 Use Taylor's polynomial of degree two about c= - 4 to estimate the value of…

A: Solved below

Q: 15. (a) Find the quadratic approximation for the function f(x) = x3/2 centered at a = 4. (b) Use…

A: 15a Given function is fx=x32. We have to find the quadratic approximation for the given function…

Q: Q.No.7 From the following table, obtain f(x) as a polynomial in powers of (x-5) using Newton's…

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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. Fınd the second Lagrange polynomial for f() = on [0, 3] using the nodes xo = 0, x1 = 1, and x2 =…

A: Given: The given polynomial is fx=11+x on [0,3] and the nodes are x0=0,x1=1 and x2=3

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: 3. Find the location and values for any global extrema of the function 1 f(x) = ³ – 2x° +5 %3D on…

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Q: Generate eight equally spaced points from the function f (t) = sin?(t) from t = 0 to 2n. Fit this…

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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: Based on the given function below x0 = 0.15, x1 = 0.25, x2 = 0.30 and x3 = 0.45 Using the…

A: As we can see points are not equidistance so we will use the divided difference method. Formula for…

Q: 1 2. Consider the function defined by f(x) = over [-1, 1]. SET-UP the Lagrange %3D 1+ 12x²…

A: Given function is fx=11+12x2 over interval -1, 1. Now 11 equally spaced nodes on -1, 1 are -1, -0.8,…

Q: 1. The specific heat capacity Cp[J/mol/°C] is often correlated to temperature T[°C] in form of a…

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Q: Consider the function f(x) = We approximate f(x) by the Lagrange interpolating 2a+1 polynomial P,…

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Q: 4 - According to table 1 values which one is the approximation of f(1.7) (just degree 1, P1 (1.7))…

A: To find the approximation of f(1.7) we will use the formula of Lagrange's Interpolation. Then we put…

Q: 3. Given the following data: 0.1 0.2 0.3 0.4 f(x) -0.29004986 -0.56079734 -0.81401972 -0.10100000…

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Q: 1 1+ 12,2 over [-1, 1]. SET-UP the Lagrange (-1, 1). 2. Consider the function defined by f(x)…

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Q: 2 - According to table 1 values which one is the approximation of f(1.7) (just degree 1, P1 (1.7))…

A: We can use the below formula to find the approximated value for x = 1.7.

Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

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Q: Q1/ The Lagrange polynomial whose curve passes through the following points y(0) = 1,y(1) = 5,y(2) =…

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Q: Xk -1 |0 |1 | 2 |f(xx) -4 -1 2 11 Table is given. a. Lagrange interpolation polynomial of degree 3.…

A: (a) Given  n=3       Therefor,Lagrange's interpolation polynomial is given by…

Q: 1. Determine the fourth-order polynomial in Newton and Lagrange form that passes through the points…

A: Given,

Q: Find T4(x): the Taylor polynomial of degree 4 of the function f(x) = arctan(11a) at a = 0. (You no

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Q: 1-2 In each part, find the local quadratic approximation of f at x = xo, and use that approximation…

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Q: 4. a) Let P3(x) (classical) be the interpolating polynomial for the data given in Table 1. Find y if…

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Q: Calculate f (3.4) using Newton.s interpolating polynomials of order 1 through 3 and estimate the…

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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: 4. If f(x) is any polynomial of degree 10, then the 9th derivative of f (x) is zero. 5. If f'(0) =…

A: A detailed solution is given below

Q: 6. Consider the function f(x) = 1 x > 0. x +2 (a) Find the interpolating polynomial P2(x) that…

A: Given :-  The given function fx = 1x+2 , x>0 (a) The interpolating polynomial P2x that agrees…

Q: 3. Given the following data: 0.1 0.2 0.3 0.4 f(x) -0.29004986 -0.56079734 -0.81401972 -0.10100000…

A: Here we use the newton’s divide difference formula and solve the given parts:   For the simplicity…

Q: 18. Find the equation of the polynomial, f), with the folle properties. * Derree is 5 • Zero at x =…

A: We have to find polynomial

Q: Use Newton.s interpolating polynomial to determine y at x= 8 to the best possible accuracy. 1 2 5.5…

A: Given data is  To find the value of y at x=8 using Newton's interpolation formula,

Q: [-x, 7] aralığı üzerinde f(x) = cos x fonksiyonunu ele alınız. f(x) için 0 and x2 = T (düğüm)…

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Q: If the data was used to create a Newton divided differences Interpolating polynomial resulted in the…

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Q: 1 2 5 7 8 f(x) 3 6 19 99 291 444 Calculate f(4) using Newton's interpolating polynomials of order 1…

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Q: 1- Using Newton's backward difference formula, construct an interpolating polynomial of degree 3 for…

A: When the value of function at certain equally spaced points is known then the Newton's backward…