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

Q: 4. Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial for…

A: To find- Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial…

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

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Q: For which value of x does the Maclaurin polynomial Tn satisfy Tn(x) = f (x), no matter what f is?

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

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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: 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 interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

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Q: determine the degree of the maclaurin polynomial required for the error in the approximation of the…

A: f(x)=cosxLet f be a real valued and differentiable function through n+1 order in an interval I…

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: Maclaurin's Series of f(x) f(x)=f(0)+xf'(0)+x22!f''(0)+ ⋯ +xnn!fn(0)+Rn(x)…

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: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: Given f(x)=sinx We have to determine the degree of the Maclaurin polynomial required for the error…

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: 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: Find the nth Maclaurin polynomial for the function. f(x) = eX, n-5 Ps(x) =

A: In this question, we want to find the maclaurin polynomial of the given function when n=5.

Q: 1) Let f(x) = e2* Find 3rd Maclaurin Polynomial for f(x)

A: Given f(x)=e2x To find the third order maclaurins polynomial

Q: If f(x)=ln(x) and x,-3.1, x₁-3.2, x-3.16, then the error bound in Lagrange interpolating polynomial…

A: Given the function is fx=lnx and x0=3.1, x1=3.2, x=3.16

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

A: In this question we have to find the interpolating polynomial by using Newton's interpolation…

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: Generate eight equally spaced points from the function f (t) = sin?(t) from t = 0 to 2n. Fit this…

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

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

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e-X, n= 5

A: A Maclaurin polynomial for a function f(x) is given by  Pn(x)=∑k=0nfk(0)k!xk. Here n=5 So, the…

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e-X, n = 4

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

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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: From the table find f(1) using interpolating of Lagrange polynomial -102 Y=f(x) 2 -1 5 1 O -1 O о о…

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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: 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: 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…

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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 value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3. y=f(x) 1…

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

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

A:

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

A:

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

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e, n- 5 Pglx) =

A: f(x)=e-x, n=5 Now P5(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+f''''(0)4!x4+f'''''(0)5!x5…

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: Given: fx=ex