Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table: x f (x) −0.1 5.30000 0.0 2.00000 0.2 3.19000 0.3 1.00000

Q: Suppose the interpolating polynomial P, (x) for f(x),on x, = i+1,Vi = 0,1,2 is P,(x) = 3 + 4(x– 1) +…

A: We are given that P2(x) interpolation f(x). So,           f(3) = P2(3) = 3+43-1+3-13-2=13 Thus, the…

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: y = exp( 2-x ) at x = [-1,2].

A: Given   y=e(2-x) , in the interval x=-1,2 So the value of y at x=-1,0,1,2 are…

Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: We have to approximate the function at the given value of x: fx=e4x,      f14 To find f14 we need to…

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: In the given question as follows, determine whether the statement is true or false. If it is false,…

A: In the given question as follows, determine whether the statement is true or false. If it is false,…

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: There is an inaccuracy in the following table of a low degree polynomial p(x). x p(x) 0.0 0.000 0.1…

A: The relationship between the data points can be observed using a difference table. Make Newton's…

Q: Let f(x) = e^x. Find the polynomial P2(x) of degree at most 2 such that P2(1) = f(1), P2(2) = f(2),…

A: We have to find the polynomial of degree 2 for the function fx=ex using the divided difference…

Q: Consider the following. Fx) = * f(x) 4 14 - 32x2 Find the critical numbers. (Enter your answers as a…

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Q: Newton interpolator polynomial

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Q: Employ the Parabolic Interpolation method to find the maximum of the following function using these…

A: Given: x0=-2, x1=-1, x2=1 f(x)=-x^4-2x^3-8x^2-5x

Q: Given the table of xi and f(xi): 0.2 0.4 0.6 0.8 1.0 1.2 f(x) 0.203 0.423 0.684 1.03 1.557 2.572…

A: The forward difference is nothing but the difference of consecutive terms. The forward difference is…

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

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Q: Use appropriate Lagrange interpolating polynomials of degrees three to approximate f(8.4) if f(8.1)…

A: x y=f(x) 8.1 16.94410 8.3 17.56492 8.6 18.50515 8.7 18.82091 We need to find f(8.4) using…

Q: Neville’s Algorithm is used to approximate f (0) using f (−2), f (−1), f (1), and f (2). Suppose f…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: Given a function f (x) that passes through the points (1, 2), (2,−1), and (3, 4), use the Lagrange…

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Q: Find the Hermite interpolation polynomial H(æ) for the following data. -9 - 8 -5 f(x) 1 f'(x) 3 H(x)…

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Q: Apply the division algorithm to find the qoutient and remainder on dividing f (x) by g (x) as given…

A: Apply the division algorithm

Q: Use appropriate Lagrange interpolating polynomial to approximate f (8.4), if S(8.1) =16.94410,…

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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: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let P2(x) be the interpolating polynomial for f(x) at xo = 0.5, x1 = 1.2, and x2 = 2. Find a bound…

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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: Given the graph of the following degree 4 polynomial function, find all of the zeros and their…

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Q: Consider the following Polynomial S(x) = x' - 3x' – 10x² + x +11 Compute the root x=1 of the above…

A: as per Bartleby's expert answering policy, we can answer only one question, so here we have solved…

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: Let p2(x) be the interpolating polynomial of f(x) at xo = 4, ¤1 = 4.5, and x2 = 5. Then, the error…

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Q: Fit the following data using Lagrange Interpolating Polynomial and compute f(x) at x=-1 X 2 6 3.2 -1…

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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: Construct the Lagrange interpolating polynomial for the following data set 0.1 0 0.2 0.4 X f(x) 0.74…

A: We have to solve given problems:

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

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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: 1#Use appropriate Lagrange interpolating polynomial to approximate f(7.2) , if f(7.1)=6.94,…

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Q: Construct the Lagrange interpolating polynomial of degree 3 for the following data. And calculate…

A: The polynomial for the data can be calculated using Lagrange's interpolation. The formula for…

Q: Consider the function f(x)=exp(x). Let p in P2 be the interpolation polynomial for the data…

A: The expression, Pn indicates the nth degree polynomial approximation of the function, y=f(x) .…

Q: Consider the following function: 3x 8x −1 -8x 3 2 -X 0 0 0 f(x) = -15 15 1 8 11 1 When f(x) is…

A: Given function is f(x) = 3x8x-151-1-8x15832-x110001

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

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Q: Let P(x) be the second degree Lagrange interpolating polynomial that fits the data (1,1), (2, -1)…

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Q: 1 2 3 4 5 6 f(x) 3 6 11 30 75 158 291 f(x) = f'(x) = f" (ε) f"'(x) = f(0.5) f'(0.5) f"(0.5)

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

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

Q: To find an nth Lagrange interpolation polynomial p(x) we need n distinct numbers and their values in…

A: To find an nth Lagrange interpolation polynomial p(x) we need n distinct nbers and their values in…

Q: Consider the function f(x)=exp(x). Let p in P, be the interpolation polynomial for the data x=(0,1)…

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

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