Consider the following data (xy): (-2, 1), (0, 3), (2, -1). Find the interpolation polynomials P(x) of least degree that interpolates the given datas. Select one: O a P(x)= O b. None of these OC P)=-x-3 O d p) ---*+3 Finish attempt-

Q: 2. Find the polynomial the passes through the following points (0,0), (2, —2), (4,0)

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Q: Explain the other notation which is commonly used for ak in the Newton form of the interpolating…

A: The Newton interpolation polynomial are calculated as: \

Q: Find a linear funtion P(z) = a + a₁ which gives the best least squares fit for the following points:…

A: Given the points -4,0, -2, -2, 4,-9, 5, -8. Now,  x y x2 xy -4 0 16 0 -2 -2 4 4 4 -9 16 -36…

Q: ind a polynomial p(x) with zeros as -2,-3,1,3 ?

A: To find a polynomial p(x) with zeros as -2,-3,1,3

Q: Explain the problems with the Lagrange form of the interpolating polynomial?

A: Lagrange polynomials are used for polynomial interpolation.

Q: Find x and y such that,  77815x - 8216y=(77815 , 8216

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Q: Find the meteix A of the Lineak teansfoRmati on foom IRto IR . 2. given by x2

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Q: Find values of a, b, and c such that the graph of the polynomial p (x) = ax2 + bx + c passes through…

A: We have to solve the value of a, b and c.

Q: A third degree polynomial passes through the points (0,9), (1.14), (2,17), (3,24), (4,41), (5,74)…

A: The value of X1=∆y3=y4-y3=24-17⇒X1=7and value of ∆2y2=X2=∆y3-∆y2=7-3=4⇒X2=4

Q: Determine the linear interpolating polynomial that passes through the points (2,4) and (5,1). p(x) =…

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Q: Interpolation is a type of estimation, a method of constructing new data points within the range of…

A: Suppose that there are three points x1,y1,x2,y2,x3,y3. The given system is:…

Q: Let fix)= 2x-3 and gix)=x?+4x-4 . Evaluate: f(-3)= gt2)= f(a-2):

A: Given: f(x)=2x-3g(x)=x2+4x-4

Q: Calculate the commutators [p(hat)x3, x(hat)].

A: We have to calculate the following commutators. p^x3 , x^ Introduction: Commutation of operator A^…

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

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Q: 2. Write a computer code that interpolates the function f(x) = 1+2 at the points -5, -4, -3, -2, -1,…

A: Here is the code:import numpy as np import matplotlib.pyplot as plt # Define the function def f(x):…

Q: State the most appropriate degree and the sign (+/-) of the leading coefficient of the following…

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Q: Then y'(0) 1- 1 2

A: Here we use Newton's Forward Difference Method :

Q: Showthat dz du

A: I am attaching image so that you understand each and every step.

Q: what is the characteristic of Z6xZ9

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Q: Define the Newton form of the interpolating polynomial?

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Q: Find iterpolation polynomial p2(x) = ax² + bx + c that passess through the points: (0,7), (1,12),…

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Q: For which function defined by a polynomial are the zeros of the polynomial-4 and-6? 1) y=x² -10x-24…

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

A: The objective is to find the interpolating polynomial of the least degree. (a)Given data is x 3 7…

Q: x* +5х + 5х + 27 х+3

A: We need to simplify x4+5x2+5x+27x2+3. So,…

Q: Find the interpolating polynomial of degree at most 2 that passes through the points (-2, 14), (1,…

A: Using Lagrange interpolating polynomial.

Q: A. List all the possible zeroes of the function below : 1.) 3x^3 - 10x^2 +4x + 5 2.) x^3 - 3x - 2 B.…

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Q: Vrite the polynomial P(x) = x-1 as a linear combination of P1(x) = 1-x+ 3x and Pa(x) =1-x+ 2x OA.…

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Q: A polynomial which goes through the point (1,4) and has zeros at x=0,x=3 and x=-2

A: Given:A polynomial pass through the point (1,4) and has zeroes at x=0, x=3 and x=-2.

Q: (b) The following list shows some values obtained from a polynomial of degree four for a particular…

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