Consider the table below to approximate f(21) using the first Lagrange interpolating polynomial (n=1) f(x) 1 40 42 10 44 15 48 18 54 22 58 Answer: LO

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: y = exp( 2-x ) at x = [-1,2].

A: Given   y=e(2-x) , in the interval x=-1,2 So the value of y at x=-1,0,1,2 are…

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Q.5: For the given data; x f(x) 1 3 2 6 3 19 5 99 7 291 8 444 Calculate f(4) and f (2.5) using third…

A: Let the given data be x0,y0, x1,y1, ..., xn,yn. To obtain the n-th order Lagrange interpolating…

Q: A function y=f(x) is given by the following table. 12 84 21 343 4 Y 2.6 26 61 a) Explain and…

A: Given:  x 0 4 7 12 21 f(x) 2.6 26 61 84 343 Divided difference is an interpolation…

Q: Use appropriate Lagrange interpolating polynomials to approximate f(1) if f(0) = 0, f(2) = −1, f(3)…

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Q: Derive the third-order Newton’s interpolating polynomial for the following data:           xi 0…

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Q: Refer to the following functions: p(x) = x2 + 2x – 15 x +1 9(x) x-3 r(x) = v7-x Which of the…

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Q: t f(x) be a function tabulated over 4 points, as shown in the table below. Using a degree 3 Newton…

A: Introduction: Extrapolation is the process of computing the value of a function outside the given…

Q: Q1) B) Use the Polynomial interpolation formula to compute f (2) from the experimental data shown in…

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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: Q4. Use Newton forward-difference formula and construct appropriate interpolating polynomial and…

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Q: Exercises: 1. Compute the divided-difference table for the tabulated function. 8 Xi 4 5 7 2.828 43…

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

Q: calculate f(4.0) using: x      0.50 1.50 2.50 3.57 4.50 f (x)  1.041 1.141 1.391 2.991 8.341 a)…

A: Hello. Since your question has multiple parts, we will solve the first  parts for you. If you want…

Q: Using the provided data, find the interpolated value of f(x) when x = 3 using Newton's Divided…

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Q: Consider the function f(x)=x+2x.f(x)=x+2x. Construct the Lagrange interpolation polynomial which…

A: Lagrange's interpolation formula for n points can be defined as:…

Q: Consider f(x) = 9x – 8. a. Compute: f(a) = b. Compute and simplify: f(a + h) c. Compute and…

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Q: Consider the functions: f(t) = 16t and 9(t) = e. Using the definition of convolution find integer…

A: Given the given functions are ft=16tgt=e4t Apply convolution f*gt=∫0tfTgt-TdT

Q: 1. Compute the divided-difference table for the tabulated function. 8 Xị 4 5 6 7 2.828 43 yi 2 2.236…

A: 1) Here n=5, We can generate the Divided - Difference table by using given formula: The First order…

Q: The following data defines the sea-level concentration of dissolved oxygen for fresh water as a…

A: Given: some given data's are missing  The given data T°C 8 16 24 32 40 O,mg/L 14.621 11.843…

Q: 2.Use the Newton interpolation polynomial to find f(0.05) based on the following data points {(-0,5,…

A: Given data is  {(-0.5,0.97939),(0.15,4.72743),(0.5,13.69506),(1,61.25661)} we have to find the value…

Q: A function ? = ?(?) is given by the following table. X    0 4 7 12 21 Y    3 30 61 84 343 a) Explain…

A: To construct the divided difference table, use the formulae fxi,xi+1=fxi+1-fxixi+1-xi,…

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: Find out the Lagrange interpolating polynomial of the first, second and third order to evaluate…

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Q: (a) Consider the table below for an arbitrary function y = = f(x). I |1|2| 3| 4 | 5 6| 7| 8 f(r) | 9…

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