1. Find the polynomial of degree three for the following data. Also find P(-2). 1 4 1 -1 1 -1 I

Q: Given the following table of data, X 6.6 6.8 7.0 7.2 7.4 f(x) 8.820 18.501 28.423 38.102 47.021 find…

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Q: Find the Newton's polynomial which interpolating the following data. 1 2 3 4 5 f(x) 3.6 1.8 1.2 0.9…

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X 0 1 4 6 -1 1 y -1

A: We have,

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

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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: In the given question as follows , find the nth Maclaurin polynomial for the function:- f (x) =…

A: Maclaurin series is a special case of Taylor's series where the specific point on which the series…

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

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Q: ● Find the best fit equation for the second-degree polynomial of the form y = ao + a₁x + a₂x² given…

A: We need to fit the polynomial y=a0+a1x+a2x2 for the data x y 1 -9 3 3 4 16 5 29 7 70…

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: Given that f(0) = 1, f(1) = 3, f(3) = 55, find the unique polynomial of degree 2 or less, which fits…

A: Solution is given:

Q: . Find the polynomial of degree three for the following data using excel. Also find P(-2). X 0 1 |4…

A: We will find out the required value.

Q: 32. The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

A: Newton's farword diffrence formula

Q: Q6) Fit a second order polynomial to the following data. Also estimate the value of y at x=1.25,…

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X0 1 4 6 -1 1 -1 1

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Q: Approximate  f′(2)f′(2) using the given data f(0)=−8,f(0)=−8, f(1)=−7,f(1)=−7, f(2)=0,f(2)=0,  and…

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Q: consider the degree 4 LFSR given by polynomial p(x)=x^4+x^2+1. What kind of polynomial is this…

A: The given polynomial p(x)=x^4+x^2+1 With 4 LFSR.

Q: Show that the polynomial interpolating the following data has degree 3. 비 f(x) 1 4 11 16 13 X -2 0 1…

A: using the dummy equation ax3+bx2+cx+d =0 and finding the value of a,b,c,d.

Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 6. X 0.4 0.8 1.2 1.6 y 00.25 1…

A: In the given question we have to define a second order polynomial to a givendata  i 1 2 3 4 5 6…

Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

A: Given: x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12 To find: Construct the…

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X0 1 4 6 -1 1|-1 y 1

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

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

A:

Q: Given the following points (–1,1), (0, –3), (1, –1), and (2,19). Let x, = -1, x1 = 0, x2 = 1, and x3…

A: Given x f(x) -1 1 0 -3 1 -1 2 19

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: 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: or the following find the function P defined by polynomial of degree 3 with real coefficients that…

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Q: Fit a cubic polynomial to the following data: X y 3 1.6 4 3.6 5 4.4 Determine the coefficients, r²…

A: Given data: let us start using cubic polynomial    X Y 3 1.6 4 3.6 5 4.4 7 3.4 8 2.2…

Q: Question 6 Determine the Charactaristic polynomial of x?y" + x?y" - 2xy' + 2y 0 OA None of the…

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). 1 4 6. y 1 -1 1 -1

A: For the given data points,we have to find out the third degree polynomial satisfying the given data.

Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 0.4 0.8 1.2 1.6 2 Ly 0 0.25 1…

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). 1 4 6. 1 -1 1 -1 I

A: We have to find the satisfying third degree polynomial.

Q: Find the polynomial of degree 3 with leading coefficient -2 and zeros at 2, 4, and -3. a) O-2- 10²…

A: The polynomial will bekx-αx-βx-γwhere 'k' is leading coefficient α,β,γ are zerossubstitute…

Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

A: A table with values x and y is given below, x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625…

Q: 2.0 Fit a cubic polynomial to the following data: 3 5 8 2.2 4 12 y 1.6 3.6 4.4 3.4 2.8 3.8 4.6

A: x y 3 1.6 4 3.6 5 4.4 7 3.4 8 2.2 9 2.8 11 3.8 12 4.6 cubic polynomial is of the…

Q: 2.3. Approximate fl1895) vising an interpolacting polynomial of degree & using Netu tons.…

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Q: Given the following table of values, use Lagrange Interpolation to find the 2nd degree polynomial of…

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Q: Q// Fit a second-order polynomial to the following data: Y 9 8 3 7 9 11 9 6 1 7 1 3 10 9. 1 a. y =…

A: Given x y 9 8 0 3 7 9 11 9 6 1 0 0 0 7 1 3 8 10 9 1

Q: Problem 1. Let be an arbitrary polynomial p(x) = anx" + an-1x"-+ . + a1x + ao. %3D (a) Find p(z)].…

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Q: Given these data X 1 2 7 f(x) 3 19 99 291 Estimate f(2.5) and f(4), (a) using an interpolating…

A: NOTE: According to guideline answer of first method can be given, for other please ask in a…

Q: 12. R sed e A fourth-degree polynomial P(x) satisfies A4P(0) AP(x) = P(x + 1) - P(x). Compute…

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Q: 4. Find the remainder of f (x) = (1 + x)3/² of degree 3.

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Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X01 4 6 y 1 -1 1 -1

A: Newton's divided differences

Q: i Yi -2 3. -1 x2-9x+8 3. 1. 1, 2.

A: Solution is uploaded here

Q: Q.3: Determine the Lagrange interpolating polynomial by using second order form for the given data…

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Q: 3. The following data come from a table that was measured with high precision. Use the best…

A: For this problem we use newton difference rule

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X01 4 6 -1 1 y 1 -1

A: This is a problem of Numerical Analysis.

Q: Q4) Fit a second order polynomial to the following data 1 2 3 4 5 X 0.4 0.8 1.2 1.6 Ly 0 0.25 1 2.25…

A: Equation of 2nd degree polynomial

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). 1 4 6 1 -1 у 1 y -1

A:

Q: Fit a second order polynomial to the following data i 1 2 0 0.4 0.8 0 0.25 1 5 6 1.6 2 4 6.25 3 4 X…

A: Let a second degree polynomial that needed to be fitted to the given data be a0+a1x+a2x2=y-----(1)…