Find the interpolating polynomial of the following point and function using Newton's interpolation process. y = ln ( x + 2 ) at x = [-1,2].

Q: Find the interpolating polynomial of the following points or functions using Newton's

A: Given: The points -2, 2, -1, -2, 1, 3 and 3, -3. To find: Interpolating polynomial.

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree polynomial for f(x) = using Lagrange Interpolation is

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Q: From the given data, identify f(4) using Lagrange and Newton's polynomial. (2,10), (3,15), (5,25),…

A: The Lagrange and Newtons polynomials can be used to find a polynomial for the given set of data.…

Q: when x = 3.57 using quadratic Approximate y Lagrange Interpolating polynomial up to 3rd degree. Use…

A: Given table is xi yi 3.1 20.1810 3.2 22.5280 3.3 25.0470 3.4 27.7440 3.5 30.6250 3.6…

Q: Approximate f(3) using an interpolating polynomial of degree 3 using Newton forward-difference…

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

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Q: For the given points X, = 1, x, = 1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial…

A: We have to find out Polynomial using given values and function.

Q: Consider the Lagrange polynomial that passes through the 3 data points given by -1 3 |f(x) | -3 9 17…

A: the given table is ;       X      f(x) -1 -3 2 9 3 17 the value of the table for x and y…

Q: Find the third order Maclaurin polynomial for f( x)= 1+ x and use it to approximate 1.1.

A: This question can be solved using McLaurin expansion till first four terms

Q: In deriving the three point formulas, we use Lagrange polynomial. L'o(x) at x = x, is (notice the…

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Q: Show that the nth Maclaurin polynomial for f(x) = e* is Tn (x) = 1+ 2! n!

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Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

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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: From a function, f(x), we obtain the following data points: (ri, f(x₂)) = {(-0.5, e³/2), (0, 1),…

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

Q: For a given data (x,f(x)):(-1.89,-4.179169),(0,-1),( 1.89,9.323369), estimate the function value at…

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

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Q: For the given points X, = 1, x =1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial for…

A: Given function is f(x)=x2esinx+ln(sinx) Find 'f(x)' corresponding to given values of 'x' x 1 1.5…

Q: 2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation…

A: Step:- 1 Lagrange Interpolating polynomial:- P(x)=f0 L0(x) +f1 L1(x)+ f2 L3(x)+....fn Ln(x),Here,…

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

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Q: Find the root of the polynomial f(x) =x® – 500 by using the Newton's Theorem, and check the root to…

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Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using xo =…

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Q: (B): For the function f(x) sinx, let x, = 0, x1 = 0.6, x2 0.9.Construct Lagrange polynomial %3D…

A: Given fx=sinx, x0=0, x1=0.6, x2=0.9. The lagrange polynomial interpolation of order 2 for a function…

Q: what is the approximate value at point x- 0.7 of the interpolation polynomial obtained using the…

A: We have the following values: x y -1 4 0 11 1 16 2 13 Now, let make the backward…

Q: For the given function 1 (x)=sin x, let x, = 0, x, = 0.6 and x, = 0.9. Construct the Lagrange…

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Q: Use Newton's interpolating polynomial to determine y at x = 4 to the best possible accuracy x 3 5.25…

A: Given: x 3 5 2 6 1 y=fx 5.25 19.55 4 36 4.65 To find: y at x=4 using Newton's interpolating…

Q: From the following table, obtain f(x) as a polynomial in powers of (x-5) using Newton's method. 2 4…

A: Given   x 0 2 3 4 5 6 f(x) 4 26 58 112 466 922     Let ,  Y = f(x) Now, Newton's divide…

Q: Find the fifth Maclaurin polynomial for f(x)=x e* and use it to estimate f(.2)

A: Maclaurin series is Taylor series evaluated at x=0. Maclaurin series of a function f(x) if given by…

Q: Q1/ Use the polynomial that fits data shown by Newton divided difference ,and estimate

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Q: Find the Maclaurin polynomial of degree 8 for the function f(x)=sin(6x)

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Q: F(x) JO sin(7t) dt.

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Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using x, = 8,…

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Q: Consider the function f(x) = x = [0,2]. Construct the , Lagrange interpolation polynomial which…

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Q: Given the function below, find the 3rd degree Taylor polynomial T3(x) centered at x = 5. Que Que…

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Q: a) Develop a table of f(x)= e¯* + 5x for x = 2, 4, 5 and 8. b) Estimate f(3.2) using the…

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

A: It is given that fx=x3. We have to construct the polynomial using the Lagrange's interpolation…

Q: In deriving the three point formulas, we use Lagrange polynomial. Lo(x) at x = x, is (notice the…

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Q: Find the Lagrange and the Newton forms of the interpolating polynomial for these data: -2 0 1 f(x) 1…

A: Given data : x   -2   0  1 f(x)    0   1  -1 Lagrange Interpolation formula: Let…

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree %3| polynomial for f(x) = using Lagrange…

A: Given function is f(x)=12and the nodes are x0=2, x1=3 and x2=4. We have to find second degree…

Q: Find the interpolating polynomial of the following point and function using Newton's interpolation…

A: Please check step 2 for the solution.

Q: Given these data, calculate f(2.8) using Newton’s divided-difference interpolating polynomial of…

A: We know that nth order polynomial of Newton's interpolating polynomial is defined as below,…

Q: Find the nth Maclaurin polynomial for the function f(x) = tan x, n = 3

A: Find the nth Maclaurin polynomial for the function f(x) = tan x, n = 3

Q: The function f(x) = cos(3x) is interpolated on the interval [О, 1/5] with a polynomial of order 3…

A: According to the given information, Consider the given function.

Q: Find the nth Maclaurin polynomial for the function f(x) = cos 3x, n = 4

A: Maclaurin polynomial: fx=∑n=0∞xnn!fn(0)f(x)=f0+xf'0+x22!f''0+x33!f'''(0)+x44!f''''(0)       For n=4…

Q: Use Newton.s interpolating polynomial to determine y at x= 8 to the best possible accuracy. 1 2 5.5…

A: Given data is  To find the value of y at x=8 using Newton's interpolation formula,

Q: Let F(x) = e -514 dt. Find the MacLaurin polynomial of degree 5 for F(x). - 0.12 -5x* dx. e Sx4 Use…

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Q: In deriving the three point formulas, we use Lagrange polynomial. Lo(x) at x = x0 is (notice the…

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Q: In deriving the three point formulas, we use Lagrange polynomial. Lo(x) at x = xo is (notice the…

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Q: Find the interpolating polynomial of the following point and function using the Lagrange…

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