1. Using the points xo = 1 , x1 = 1.6, and x2 = 2.5, find the Lagrange interpolating polynomial that fits the function 2/x

Q: Let P(x) be the Lagrange interpolating polynomial of 1 f(x) = ; 2x² + 2 at the points xo = 0; x, = 1…

A: We will use La Grange interpolation

Q: Find the quadratic Lagrange polynomial for the data in the table below, and use it to compute…

A: Given table: x 0 1 2 fx 0 1 8 The objective is to find the quadratic polynomial and then to…

Q: When calculating the first Lagrange polynomial using xo, X, we obtain L,(x) = x – 3, then Xo and x1…

A:

Q: For the given points X, = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial ww…

A:

Q: Given the following data which generated by the function y = 1/x. %3D X 1 2 4 5 y=f(x) 1 0.5 0.3333…

A:

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: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 4 P4(x)

A:

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

A:

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Find the the Taylor's polynomial P2(x)for the function f(x) = 5x2e-2 about xo = hence find f(0.5).…

A: Given, f(x) =5x2e-2xThe Taylor's polynomial P2(x) about x…

Q: Consider the following table: Xi 5 6 f(X) 7 12 14 Find f(4) using Lagrange method for interpolation.…

A:

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 nth Maclaurin polynomial for the function. f(x) = sin(x), n = 5 1. 2 1- x+ x - 1.4 24 1 5…

A: We have to solve

Q: 4. a) Find the second Taylor's polynomial P2(x) approximating the function f (x) = e2* + cosx about…

A: Given function is fx=e2x+cosx.

Q: The Lagrange polynomial that passes through the four data points is given by x 15 18 22 30 y 24 37…

A:

Q: 9) Find the cost of estimating f(x) using Lagrange interpolating polynomial p2 (x) for a specific…

A: To find: Cost of estimating fx¯ using Lagrange interpolating polynomial P2x for a point x¯. We shall…

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3 7. y=f(x)…

A: If y=fx takes the values y0,y1,....,yn corresponding to x0,x1,....,xn then the Lagrange's…

Q: Let P(x) be the Lagrange interpolating polynomial of f(x)%3= 3x +3 at the points Xg 0: x 1 and x; =…

A: 1/15 is the answer.

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: Let P(x) be the Lagrange interpolating polynomial of 1 f(x) = at the points xo = 0; x, = 1 and x =…

A:

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 1 3 5 7 2…

A: See the attachment.

Q: (a) Develop a table of f(x)=2e* + 3x for x = 3, 5, 7 and 9. (b) Estimate f(4.2) using the…

A:

Q: 4. For the given function f(x) = /2 + x², let xo = 0, x1 = 0.5, and x2 = 0.8. Construct a Lagrange…

A:

Q: Find the second Taylor polynomial for the function f(x) = x² – 2x + 1 about xo=0, and hence find…

A: We use the definition of the Taylor polynomial of a function centred about x=a to answer the given…

Q: Determine an approximate value of f(1.22) utilizing Lagrange interpolating polynomial of degree four…

A:

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

A:

Q: 7. a) Use the appropriate Lagrange interpolating polynomial of degree two P,(x) to approximate…

A: Given f0.1=0.665, f0.2=0.8, f0.3=1.8, f0.4=0.25

Q: 2. y = cos ( 2x ) at x = [0,r] with four equally spaced points. %3D

A: The interpolation techniques are used to establish the functional relationship between any two…

Q: The Lagrange polynomial that passes through the four data points is given by 15 18 22 30 y 24 37 25…

A:

Q: Let P(x) be the Lagrange interpolating polynomial of f(x) = x³ – 3x + 3 at the points x, = 0; x, = 1…

A:

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

A:

Q: Use the numbers (called nodes) x_0=2, x_1=2.75, and x_2=4 to find the second degree Lagrange…

A:

Q: 2. if √o = √T = 1 and √4 = 2 estimate √3 to by constructing Lagrange polynomial, then compare with…

A:

Q: if √0 =0, √T = 1 and √4 = 2 estimate √3 Compare by constructing Lagrange polynomial, ther with the…

A: Let  f(x)=x We have x f(x)=x 0 0 1 1 4 2 we have x0=0, x1=1, x2=4 Lagrange's polynomial…

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: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

Q: Use appropriate Lagrange interpolating polynomial for the following table and approximate f(1.5) Xi…

A:

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

A:

Q: J(x) x cos (2x), To (a) Find Lagrange interpolating polynomial for f(x) using the three given nodes…

A: Given : fx=x cos2x -x2           x0 =0 ,  x1=0.3   x2=0.7 To Find :  Lagrange interpolation…

Q: 6. For f(x) = 2x - x, construct the second Lagrange interpolating polynomial using the nodes xo = 1,…

A: Given as, f(x)=e2x -x x0 =1,x1 =1.25,x2 =1.6.

Q: for the function f (x) = x + . Estimate a) Lagrange interpolating polynomial b) Newton's…

A:

Q: Find the the Taylor's polynomial P2(x)for the function f(x) = 4x²e¬2« about xo = 0 and hence find…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: For the given points Xo = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial for…

A: Given: The function is  f(x)=x2esin x+ln(sin x) The points are x0=1, x1=1.5, x2=2.5, x3=3   To…

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: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 5 P5(x) = sin(5)

A:

Q: 1. For the function f(x) = /1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Con- struct Lagrange…

A: Given:

Q: Suppose that Pɔ(x) is the second degree Lagrange interpolating polynomial for the data: 1 2 Yi 3 6…

A:

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

A: