Find the interpolating polynomial of the following point and function using Lagrange interpolation process. 1. (-3,0), (-1,2), (0,-2), (1,3) and (3,-1). 2. y = cos ( 2x ) at x = [0,π] with four equally spaced points.

Q: 1.a) Find the Lagrange interpolation polynomial f (x) such that f(1) = 11, f(3) = 5, f(4) = 3. b)…

A: Lagrange's Interpolation: Consider the data set x0, y0, x1, y1, x2, y2, ⋯, xn, yn. The Lagrange's…

Q: 4. Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial for…

A: To find- Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial…

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: Find the Hermite interpolating polynomial for the function f(x) = √x satisfying the conditions…

A: According to Hermite interpolation the error is given by:…

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

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Q: Find the polynomial P1(x) = a0 + a1x whose value and slope agree with the value and slope of f(x) =…

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Q: Given the two points (x, V) and (x, y), the Lagrange polynomial is P (x) that passes through X-X.…

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Q: QY.Determine the root of f (x) 3x-2e by: (a) Using the bisection method. Start with a3D 0 and b= 1,…

A: f(x)=x-2e-x We need to perform the three iteration of by section method and 3 iterations of secant…

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Determine the first and second degree Maclaurin polynomial approximations, L(x, y) and Q(x, y), for…

A: f(x,y) = xx+y + xcosxyTo find: L(x,y)  = first degree Maclaurin approximationQ(x,y) = 2nd degree…

Q: For the given points X, = 1, x, = 1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial…

A: We have to find out Polynomial using given values and function.

Q: Let f(x) = x cos (2x) – x², To = 0, T1 = 0.3, r2 = 0.7. (a) Find Lagrange interpolating polynomial…

A: let fx=x cos2x-x2 with x0=0 , x1=0.3 and x2=0.7 (a) find the lgrange interpolating polynomial for fx…

Q: Let f(x) = -z cos (2.r) + a, ro = 0, a1 = 0.3, 2 0.7. (a) Find Lagrange interpolating polynomial for…

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Q: Find the Taylor polynomial T3 for the function f(x) at the numbe sin(9) + cos(9)(x-9). sin (9) +…

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Q: Find the interpolating polynomial of the following point and function using Lagrange interpolation…

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: The following table shows data of velocity versus time that has been collected by an engineer in a…

A: The Lagrange's polynomial that passes through the points x0, y0, x1, y1, x2, y2 can be estimated…

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

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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: For the given points X, = 1, x =1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial for…

A: Given function is f(x)=x2esinx+ln(sinx) Find 'f(x)' corresponding to given values of 'x' x 1 1.5…

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: Find the Taylor polynomial T,(x) for the function f centered at the number a. f(x) = 7 tan-(x), a =…

A: Given:

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: 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: Calculate the Taylor polynomials T2 and T3 centered at a = 3 for the function f(x) = x* – 5x. (Use…

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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: Given the following points (–1,1), (0, –3), (1, –1), and (2,19). Let x, = -1, x1 = 0, x2 = 1, and x3…

A: Given x f(x) -1 1 0 -3 1 -1 2 19

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: Q) Use the Lagrange interpolating polynomial of degree two to approximate f (0.43) if f (0)=1 f…

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Q: 7. a) Use the appropriate Lagrange interpolating polynomial of degree two P,(x) to approximate…

A: Given f0.1=0.665, f0.2=0.8, f0.3=1.8, f0.4=0.25

Q: We consider the following Polynomial Approximation Problem. Given distinct nodes xo,..., Xn €R and…

A: Consider the equation

Q: 2. y = cos ( 2x ) at x = [0,r] with four equally spaced points. %3D

A: The interpolation techniques are used to establish the functional relationship between any two…

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

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Q: 6a. Find the Taylor polynomial of degree 4 centered atx = 4 of f(x) = Vr. Vェ 3 !3/2 2+ 15 2! - 5/2…

A: Consider the function  fx=xx=4

Q: If the polynomial P(r) is the nth Taylor's polynomial for f(r) about the point zo then the upper…

A: Given: If the polynomial pnx is the nth Taylor's polynomial for fx about the point x0 then the upper…

Q: Q1) Use the appropriate Lagrange interpolating polynomial of degree two P2(x) to approximate f…

A: It is a Numerical analysis problem and let us use Lagrange interpolating polynomial to approximate…

Q: Let P(x) = 20x* - 7x³ be the Lagrange interpolating polynomial that approximates a function f over…

A: Sol: Px=20x4-7x3Since it approximate the function -1,1Approximation of ∫-11fxdx mus t be equal to…

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

A: Please check step 2 for the solution.

Q: From the table find f(1) using interpolating of Lagrange polynomial -102 Y=f(x) 2 -1 5 1 O -1 O о о…

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Q: J(x) x cos (2x), To (a) Find Lagrange interpolating polynomial for f(x) using the three given nodes…

A: Given : fx=x cos2x -x2           x0 =0 ,  x1=0.3   x2=0.7 To Find :  Lagrange interpolation…

Q: 2. Construct the Lagrange interpolating polynomial of order at most two P,(x) of f(x) using the…

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Q: for the function f (x) = x + . Estimate a) Lagrange interpolating polynomial b) Newton's…

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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: Find the nth Maclaurin polynomial for the function f(x) = cos 3x, n = 4

A: Maclaurin polynomial: fx=∑n=0∞xnn!fn(0)f(x)=f0+xf'0+x22!f''0+x33!f'''(0)+x44!f''''(0)       For n=4…

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: For the given points Xo = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial for…

A: Given: The function is  f(x)=x2esin x+ln(sin x) The points are x0=1, x1=1.5, x2=2.5, x3=3   To…

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

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Q: The function f(x) = cos(3x) is interpolated on the interval [0, 1/5] with a polynomial of order 3…

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