If the Newton's Divided Difference second order polynomial for the coresponding x, y data is represented by P2 (x) = a, + a, (x – 12) + az(x – 12)(x – 15), then find the value ao + az + az nearly. 12 15 21 25 36 27 A.) 25 B.) 20,644 C.) 22,811 D.) 28,092 E.) 27,977

Q: Find the interpolating polynomial of the following points or functions using Newton's

A: Given: The points -2, 2, -1, -2, 1, 3 and 3, -3. To find: Interpolating polynomial.

Q: Given P = (4, – 4) and Q = (3, – 4), find the components of PQ PQ =

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Q: Two polynomials are defined in MATLAB as >>p=[5 03 2 0]; q= 0 -1]; lo find the zeros of T(s) =…

A: Matlab is a programming and numerical platform to compute values, analyze , create model.

Q: type represented by the data? know.

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Q: Consider the data in Table. Using direct fit polynomials, calculate P₂(4.25) using: (a) the first…

A: Given: A data in the table. x F(x) 3 3.3333 3.5 3.7857 4 4.2500 4.5 4.5222 5 5.2000…

Q: B: Fit a second order polynomials to the data in the following: 5 6 7 12 13 10 X Y 1 4 3 mco 8 4 10…

A: Solution :-

Q: For the numbers 12, 13, 15, 17, 20 Compute: SX   SX2   (SX) 2

A: Given data is12, 13, 15, 17 , 20

Q: 2. Given the points (1,0.7),(2,0.73),(3,0.8),(4,0.75),(5,0.6). Use Lagrange polynomials to find the…

A: Given points are xi 1 2 3 4 5 yi 0.7 0.73 0.8 0.75 0.6 Here, i=0, 1, 2, 3, 4.

Q: If the Newton's Divided Difference second order polynomial for the coresponding x, y data is…

A:

Q: Given the following points: (0,2), (1,3) and (3,3). The Newton's divided difference interpolation…

A: We can solve this using newton interpolation formula

Q: Use Lagrange interpolating polynomials of order 4 to calculate (7.1) 1 3 8 Ax) 1 20 94 267

A:

Q: Use Newton’s Divided Difference Formula to interpolate f (1), if the polynomial has given points…

A: We have to interpolate f(1) using Newton's Divided Difference Formula.

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

A:

Q: 1. From the following data, perform the required fitting. i 1 2 4 6. 3 9 X 12 14 Y 15 21 27 36 42 a.…

A: a. Tabulate the given value as follows, x y 3 9 5 15 7 21 9 27 12 36 14 42

Q: Expand: Write as a polynomial. (2x - 3y)

A: Given,2x-3y4=2x-3y22Using,a-b2=a2+b2-2abtherefore,=2x2+3y2-22x3y2=4x2+9y2-12xy2Now,using,a+b+c2=a2+b…

Q: 4. which polynomial is accurate x = [2; 2.75; 4]; y = [0.5; 1/2.75; 0.25]] 0.0455 x² 0.1039x² -…

A:

Q: х-2 y = at [-1,1] x²+1

A: The given problem is to find interpolating polynomial for the given function and interval using…

Q: Let P(x) be the interpolating polynomial for the data (0, 1), (1,3), (4, -3). Then P(2) = 3 4 -3 1

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Q: 5. Find the best fit by a first degree polynomial for the following data: x -3 -1 0 2 y 8 5 4 1

A:

Q: If the Newton's Divided Difference second order polynomial for the coresponding x, y data is…

A: Suppose a second degree polynomial passes through three data points  . x x0 x1 x2 y=f(x) fx0…

Q: Let plx) be the Lagrange interpolating polynomial that C-2,3), (2,4), (4,3) Aits the data the n P(3)…

A: See the attachment

Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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Q: 4) The following data are given. Firstly, write the general formula of the third-order Newton's…

A: First, write the general formula in terms of x0 , x1 , x2 , x3 . Then make the divided difference…

Q: Q4. Find the interpolating polynomial of least degree that interpolates these sets of data: 3 7 a)…

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Q: Given a set of three data points {(0, 1), (2,5), (4, 17)}. Determine Newton's interpolation…

A: We have: x 0 2 4 y 1 5 17 We make a table of Newton's forward difference : x y ∆y ∆2y 0…

Q: Let consider given points: (0, 1), (2,3), (3,0). (a) Use Lagrange interpolation to find a polynomial…

A: Note: “Since you have posted multiple questions, we will provide the solution only to the first…

Q: Q4) Fit a second order polynomial to the following data 5 6 1.2 1.6 4 6.25 i 1 3 4 0 0.4 | 0.8 0…

A:

Q: Write the equations of the polynomial given the following zeros: 16. 5, – 3i

A: We have to find the equation of polynomial.

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Q: Construct the addition table for Zs. Using this table, or otherwise, determine the following x in…

A: Solution:

Q: The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in the…

A:

Q: 16. La(z) = -7 + 57z - 134z + 78 is the degree (at most) 3 interpolating polynomial for the dala in…

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Q: Find y(5) if a second-degree polynomial is fitted to the data points (1, 4), (2, 6), (3, 9), (4,…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.