a) Use Newton interpolation to find the unique cubic polynomial f that passes through the points (0, 1), (1, 1), (2, 1), (3, 4). If we write f as a linear combination of binomial polynomials f(x) = E a. (), what is the coefficient a2 ? %3D O 1 O -2 -3 2)

Q: a 3. 3 Suppose that 2 2 where x is denoting the cross-product. b Then a = and b

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Q: 1. Determine a possible equation for each polynomial function. a) f(x)= d) f (x) = c) f(x) = f) f…

A: To find the equation of the given graph of function f(x) :-

Q: Find the linear polynomial p(x) = a1x + ao, that interpolates the two points with coordinates (3, 0)…

A: Given query is to find the equation of the line.

Q: A polynomial expression is given. 3z (zy) 21'y Which is an equivalent form of the expression? 3y 3y

A: Explanation of the answer is as follows

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Firstly make the divided difference table x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl Pxi ,…

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: 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: Also, our definition of the first 4 Legendre polynomials is: 1 Po(x) V2 P1 (x) = V5/2 (1 – 312)…

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Q: a) Let P3(x) (classical) be the interpolating polynomial for the data given in Table 1. Find y if…

A: Note: Since you have posted multiple questions, according to our policy, we are only supposed to…

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x2…

A: The objective is to find the value of 2c3-c2

Q: 1) Factor f(x) = 2x3 + (-3-2i)x? + (-3- i)x + (2 + i) into linear factors 2 +i is a zero of the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7) Determine the polynomial by Newton's forward difference formula from the following table: x y 0…

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Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

A: In this question, the nested algorithm to convert the polynomial 1+2x+3x2 into its equivalent Newton…

Q: Consider the data given below: x 0 2 3 f(x) 7 11 28 (i) Find the Lagrange interpolation and Newton…

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Q: 1. What degree are the following polynomials (3.a and 3.b) and monomials (3.c and 3.d)? (a) f(æ) =…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

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

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Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Newton's Divided Difference table is given by x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl…

Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: The set of polynomials {1, x² + 3x“, 2x² – 7x4} is a linearly independent set in P4.

A: NOTE: Due to time limit answer of 1 is given here, for other please ask in a different question.…

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x2…

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Q: Prove that the polynomial f(x) 2an +a2", n € N, a E R \ {0} is not divisible by g(z) = r+a

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

A: Here are 2 ways to solve find the solution In 2 method we will use this lagrange interpolation…

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: 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: Find the Lagrange interpolating polynomial for this table 2 2.5 34 -1/3 3/32 4/3 25 I Y

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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: Find a fourth degree polynomial that has zeros of 1, -3, 2i.

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Q: Use Cramer's rule to find only the value of x2 , where a is a positive real number. 2x2 – x3 + x4 =…

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Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…