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

Q: Use this interpolating polynomial for the data points f(x) 1 0-368 1-2 0-301 1-3 0-273 1.5 0-223 To…

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

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

A: Given: A number of data points X,Y.   To determine: The value of Y at X=-7.5 using the direct method…

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

A: The Maclaurin polynomial for the function f(x) is given as: fx=f0+f'01!x+f''02!x2+f'''03!x3+ ⋯…

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: Find the nth Maclaurin polynomial for the function. 2x - 5 f(x) n = 4 %D x + 1

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Q: Allow T2(x) be the 2nd degree Tylor polynomial for the following function: f(x)=2+x*e^(5x) which is…

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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: 1. Identify which of the following are polynomial functions and, for those that are, specify the…

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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: Consider the following polynomial. h(x) —D 7x3 — 9х2 — х — 15 Step 2 of 2: Describe the behavior of…

A: Given polynomial is- h(x)=7x3-9x2-x-15 To describe the behavior of the graph of h(x) as x→±∞

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: NUMMTD PROBLEM 2: Evaluate the polynomial y = x³ – 5x² + 6x + 0.55 at x = 1.37, use 3 significant…

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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: Given these data X 1 2 3 f(x) 3 6 19 99 Estimate f(2.5) and f(4), (a) using an interpolating…

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Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) = n = 4 x + 1 P4(x) =

A: A Maclaurin polynomial of nth order  for the function f(x) is               f(x) = ∑n=0∞fn(0)n!xn,…

Q: Q9 Find the polynomial interpolating the points f(3) by using Lagrange method 2.5 4 F(x) 0.33 0.38…

A: Formula for Lagrange's interpolating polynomial is :…

Q: In the given equation as follows , find the nth Maclaurin polynomial for the function. f (x) =…

A: Given: f (x)=x2e-x for n=4

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: 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: We consider the following Polynomial Approximation Problem. Given distinct nodes xo,..., Xn €R and…

A: Consider the equation

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: 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: The following x-y data is given 10 13 15 y 50 | 113 | 165 The Newton's divided difference second…

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Q: Q// Fit a second-order polynomial to the :following data Y 7 11 7 5 2 10 4 7 2 11 11 3 y = 8.440138…

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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: 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: If R₂(x) is the second degree Lagrange interpolating polynomial for the data Xi Yi where the…

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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: The Lagrange polynomial that passes through the 3 data is given by 15 18 22 y 24 37 25 2 (x) = 24L1…

A: The three point interpolation formula through the points x0, y0, x1, y1, x2, y2 can be defined as…

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

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Q: Find the critical points, A and B, of the following polynomial (with A<B). f(x)=2x^3−24x^2+5 A=B=

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Q: Which of the following polynomial functions is/are odd function(s)? a) y--2x* - 2x + 5x – 2 b) y--2x…

A: A function y=f(x) is even if f(-x)=f(x) and odd if f(-x)=-f(x) . Substitute -x for x in the equation…

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: Find the nth Maclaurin polynomial for the function. 5x - 4 f(x): n = 4 x +1 P4(x) =

A:

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: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) n = 4 x + 1 P4(x) = =

A: The function is  f(x)=4x-5x+1

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)…