10 In each part, use the Lagrange interpolation formula to construct the polynomial of smallest degree whose graph contains the following points. (a) (-2, –6), (-1,5), (1, 3) (Ъ) (-4, 24), (1, 9), (3, 3) (c) (-2,3), (–1, –6), (1,0), (3, –2) (d) (-3,–30), (-2, 7), (0, 15), (1, 10)

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

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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: Given data:   0 1 2 x -2 2 4 y 3 4 3

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: polynömial that passes through the three points (0, 1), (1, 2) and (2, 23). If the coefficient of x…

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

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

A: We have to find zeros of polynomial

Q: 22/By using Newton's backward difference formula, construct an interpolating polynomial from the…

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Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

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Q: 10) Find the cost of evaluating p2(x), for a specific x, where p2(x) is the Lagrange interpolating…

A: The cost of p2 (x) for a specific value of x will be given by following formula-

Q: find a formula for the polynomial p(x) with degree 3 leading coefficient 1 zeros at 3, -5, and 8

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Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

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Q: Let P(x) be the second degree Lagrange interpolating polynomial that fits the data (0,0), (1,2) and…

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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: Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced…

A: In the question it is asked to construct interpolating polynomial using the table given in question.

Q: To estimate the bound of error for order one in lagrange interpolating .polynomial we…

A: solution

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

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Q: 1. Consider the following data points (0,3), (1,0), (2, 1), (3,0) (a) Derive the monomial…

A: Given data point is (0, 3), (1, 0), (2, 1), (3, 0) Solution a: For 4 data point, monomial basis,…

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: Determine the linear Lagrange interpolating polynomial that passes through the points (2, 4) and (5,…

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Q: (b) Show that factorial polynomial corresponding to P,- k³ – 4k* + 2k³ – k² + k + 10 is P, = k(5) +…

A: Given: The given polynomials is Pk=k5-4k4+2k3-k2+k+10, To prove Pk=k5+11k4-k3-9k2-k1+10

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: 13. Let P(x) be the degree 10 polynomial through the 11 points (-5,5), (-4,5), (-3,5), (-2,5),…

A: We will find the value of P(6) using the Newton's forward difference interpolation polynomial of…

Q: 4.9 (a) Evaluate the polynomial y = x – 7x + 8x – 0.35 | at x = 1.37. Use 3-digit arithmetic with…

A: Answer for sub question a: First determine the powers of x needed for evaluating the polynomial.…

Q: consider the function y=ax2+bx+c, where a is in the set {n∈ℕ|(n|15)}, b is an integer less than 10,…

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Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial…

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Q: Using the given data, we see the largest change in Y is between X = -8 and X = -7. Y X 19.1 0 19.1…

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Q: Form the polynomial function that has the following real ZEROS: 3,-1, 2, 4 Section 3.1 O z4 + 2z3 -…

A: Given point is; x = -3,-1,2,4   1) x4+2x3-14x2-13x+24  we find the factor of this function and then…

Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: In the characteristic polynomial (3 – A)(4 – A)³(–3- )(3 – 1), what is the multiplicity of d = -3?

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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: Let P(x) be the Lagrange interpolating polynomial that fits the data (1,2): (4, 3) and (7, 3). Then…

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Q: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

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Q: snip

A: Given{x,2x-x2,3x+2x2}To check dependentIf they are dependent , need to express  one function in…

Q: Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.) x =…

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Q: 2. Determine the stability of the following polynomials and the range of K that results in a stable…

A: We have to determine the stability of given polynomial equation and range of k

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

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Q: 10) Use Lagrange coefficient polynomial L3,2(x) to find L3,2(5) using the nodes Xo = 3,x1 = 4, x2 =…

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Q: consider the function y=ax2+bx+c, where a is in the set {n∈ℕ|15}, b is an integer less than 10, and…

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Q: In the characteristic polynomial (3 - A)(4 – 1)³( – 3 – )(3 – 1), what is the multiplicity of A = 4?

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Q: 4. Which of the following describes the end behavior of the polynomial y = -x+ x? A as x -oo, y 00…

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Q: Which of the following polynomials has zeros at x = -6 (which is a bounce point), and x = 4 (which…

A: Given data  Polynomial has zeros at x=-6(bounce point) Polynomial has zeros at x=4(cross point)…

Q: 2-Suppose that you have n data points (x1, y1), ..., (xn, yn), with the xi all distinct. Which of…

A: Question 2 is related to Existence and Uniqueness of interpolating polynomials Question 3 is asking…

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

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

Q: Q3. Use Lagrange interpolating polynomials of degree three to approximate f0) if it passes through…

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Q: In the set of polynomials in the form: P(x) = ax + bx' + cx² + dx + e, x E R there is a subset M,…

A: Given the polynomial M=px=ax4+bx3+cx2+dx+e, x∈ℝ|x,p(x)=-2,4,-1,0,1,-2,3,6. (a) Consider a cubic…

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: 1. Use the numbers x, =1 , x, = 2 and x, = 3 to find the second Lagrange interpolating polynomial…

A: We have x0=1, x1=2, x2=3 The polynomial is fx=x-2=1x2 Therefore,…