y = exp( 2-x ) at x = [-1,2].

Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = xe-6x, a = 0…

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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 nth Maclaurin polynomial for the function. f(x) = e¯X, n = 5 Ps(x) = %3D MastarIt

A: Given

Q: Find the second Lagrange interpolation polynomial that fn tercepts f(x)= x2+xe*+sînx at points xo=0,…

A: NOTE: A, B and C are not subparts, they are options and we have to choose the correct one.  We have…

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: Find the Hermite interpolating polynomial for the function f(x) = √x satisfying the conditions…

A: According to Hermite interpolation the error is given by:…

Q: Use the given data, for some function y, to construct the Lagrange interpolating polynomial of the…

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Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: We have to approximate the function at the given value of x: fx=e4x,      f14 To find f14 we need to…

Q: * find f(3) from the following table by Lagrange polynomial X 2 2.5 4 Y=f(x) 0.5 0.4 0.25 0.264 O…

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

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

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

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Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: Construct the Lagrange interpolation Polynomial for the function Y= Sin Tx, the ponts =0, 2, =…

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Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: Let ro = -a; xi = 0; and x2 = a. Compute the interpolation polynomial for f(x) = -r* using Lagrange…

A:

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

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

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Q: Use the numbers x, = 2 , x, = 3 and x, = 4 to find the second Lagrange interpolating %3D polynomial…

A: First of all we have to find the second Lagrange interpolating polynomial for f(x)=1/x Then we have…

Q: Determine the third Taylor polynomial of the function at x = 0. fox) = 3 X+3 01 1 3 81 01.1 x3 81 x+…

A: Given: fx = 1x+3 To evaluate: Third Taylor polynomial at x=0 In the third degree of Taylor…

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

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: 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: For f(x) = ²x - x, construct the second Lagrange interpolating polynomial using the nodes xo = 1, x₁…

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

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Q: . Suppose that f is a polynomial of degree 1 and s1, is the linear spline that interpolates f at the…

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Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = a = 4 T3(x) =

A:

Q: Q1) Use the appropriate Lagrange interpolating polynomial of degree two P2(x) to approximate f…

A: It is a Numerical analysis problem and let us use Lagrange interpolating polynomial to approximate…

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

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

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

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Q: · Construct the Lagrange interpolation polynomial for the data 1 2 -1 f(x) 1 1 5 -1 Hence,…

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Q: Calculate the Tayorl Polynomials T2(x )and T3(x) centered at x=a for the function f(x) = 7ln(x+1),…

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Q: Determine all Taylor polynomials for f(x) = x^2 + 2x + 1 atx = 0.

A: Given: fx=x2+2x+1 x0=0

Q: The Lagrange polynomial interpolating the function f(x) = 1 + x + x + x at the nodes 0, 1 and 2 is

A:

Q: Consider the function f(x) = 12, x = [0, 2]. Construct the Lagrange interpolation polynomial which…

A: Given function is fx=x21+x2, x∈0,2. We have to construct the Lagrange's interpolation polynomial…

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

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Q: Construct the Langvange inter po lation polynomial for the function y= Sin Tx, taking the points %3D…

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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: Given the Taylor polynomial for f(x) at x = 3, find ƒ(³) (3) T₁(x) = 1 + x −3+2(x − 3)² + 2(x-3)³ -…

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Q: Q3. Prove that if g interpolates the function f at ro, T1, . .. , In-1 and if h interpolates f at…

A: We have to prove that if g interpolates the function f at x0,x1,…,xn-1 and if h interpolates f at…

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: Using the two points (x,y) and (x₁,51) to find Lagrange interpolating polynomial, L.(x1) is always…

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

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Q: Find the upper bound for the absolute error on the interval [xo, x4] for the Hermit polynomial…

A: Given:- f(x)=cos x x0=1 , x1=1.1

Q: 1. Use the numbers x, =1 , x, = 2 and x, = 3 to find the second Lagrange interpolating polynomial…

A: We have x0=1, x1=2, x2=3 The polynomial is fx=x-2=1x2 Therefore,…

Q: For f(x) = 2x - x, construct the second Lagrange interpolating polynomial using the nodes xo = 1, x₁…

A: The second order Lagrange's interpolating polynomial for 3 points can be defined as:…

Q: Find the linear interpolation Lagrange polynomial P1(x) using the following data: (Xo.Yo) = (0, -1)…

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