e. S. 1. Question # 1: Consider the function f(x)= xe. In the following, the interpolating polynomial, p.(x), is computed by using Taylor expansion. To do so, do the following tasks: Find the values of a, a,, a, if the function is interpolated by degree three polynomial p.(x). Compute: f(0.1) and p3(0.1) up to seven significant figures. Find the percent error for interpolating f(x) by p.(x).

Q: 1. -1 0 1 2 f(Xx)| -4|-1 2 11 Table is given. a. Lagrange interpolation polynomial of degree 3. b.…

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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: 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: 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: 1. Using the points xo = 1 , x1 = 1.6, and x2 = 2.5, find the Lagrange interpolating polynomial that…

A: We find the Lagrange interpreting polynomial using the given points and that fits the function 2/x2.

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: Give an interpolating polynomial for f(x) = ²x at x = 0, 1 and 3. Evaluate it at x = 2 and give the…

A: The given function is: fx=e2x. The points are: x=0,1,3. Find the Lagrange polynomials.…

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: Let ro, r1,..., r10 be 11 distinct values. Let L10,i(x) (i = %3D 0,..., 10) be the polynomials for…

A: Lagrangian polynomial: If x0,x1,...,xn are any n+1 distinct numbers, then for i=0,1,...,n, the i-th…

Q: 1. Using x, = 1,x1 = 2,x2 = 3, and x3 = 4, find the Lagrange interpolating polynomial of In(x + 1).

A: Given function is f(x)=ln(x+1) Evaluate value of function at given set of points: x 1 2 3 4…

Q: Use the Product Rule to find a formula for (fg) ,,, and compare your result with the expansion of (a…

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Q: E Consider the function f(x) = [1,1]. Construct the interpolation polynomial which interpolates the…

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Q: Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5 , x, =4…

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Q: [Q1] The following table shows the distance measured for a given time seconds in a car race Time (t)…

A: 1. We must find polynomial of the form S(t) = a + bt + ct2   Where, S represents the distance, a, b,…

Q: 2Q. (b) The set of following data points is given x 1 1.5 2 5.2 y 3.8 4.9 Determine the second order…

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Q: M- 03. Determine the real root of f(x) = -26 + 85x – 91x? + 44x – 8x* + xS: a. Graphically. b. Using…

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Q: [C] Obtain the interpolating polynomial of the form a³ + bx² + cx + d (where a, b, c, d are…

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Q: [D] Use Lgrange's interpolation formula to find a polynomial in the form (az + b)(cz² + dx + e) for…

A: Using Lagrange Interpolation…

Q: Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3…

A: We use Newton's Divided Difference Interpolation Formula.  x             x0            x1…

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

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Q: Use the Newton forward difference formula to construct interpolating polynomials of degree three for…

A: Given f-0.75=-0.0718, f-0.5=-0.0247, f-0.25=0.3349, f0=1.1010

Q: Let y = x3 + x2 + A . Construct a difference table from x= 0,1,2,3, and 4. Calculate y for x=4.5 by…

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