1. For the function f(x) = /1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Con- struct Lagrange interpolation polynomial of degree at most two to approximate f(0.45), and compare the error.

Q: let f(x)=ex for 0 < x < 1 Approximate f(0.25) using linear interpolation with x0=0  and x1=0.5 .…

A: Substitute x0=0 and x1=0.5 in fx=ex  and calculate L0(x) and L1(x), to construct the Lagrange…

Q: Let g (x, y) = 7 sin(xy) – 9x? In(y) + 4. Find the degree 2 polynomial, p, which best approximates g…

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Q: Q1: For the given function f(x)= sin 7 x, let x, = 1,x, = 1.25, x, = 1.6. Approximate f(1.4) by (1)…

A: Interpolation is the construction of new values using existing values where the arguments of the new…

Q: B/ Given a polynomial function with following data points: Find x f(x) 0 3.6 1.5 1.8 3 1.2 4.5 0.9 6…

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Q: 1. For the given functionsf(x), let xo= 0, x1=0.6 and x2=0.9. Construct interpolation polynomials of…

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Q: 1) For the function f(x)=10-0.1x² +1.6x² – 4.8x on 0<x<10 and n=5: Begin by calculating Ar and…

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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: Determine the first and second degree Maclaurin polynomial approximations, L(x, y) and Q(x, y), for…

A: f(x,y) = xx+y + xcosxyTo find: L(x,y)  = first degree Maclaurin approximationQ(x,y) = 2nd degree…

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: If f(x) = e", then the third Taylor's polynomial P3(x) at ro = 0 will be

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Q: 4. (S.15). For the given function f(x) = v2+r2, let ro = 0, r1 = 0.5, and r2 = 0.8. Construct a…

A: Given f(x) = 2+x2 Hence x f(x) 0 2+02 = 1.414 0.5 2+(0.5)2 = 1.5 0.8 2+(0.8)2 = 1.625…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

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: 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: 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: The Taylor polynomial of the function f(x)= e* up to order 3 about X = 0 is given by 1- x+x²- 6 a O…

A: Given function is f(x)=e^2x

Q: 3 Given f(x) = Vx+ 5 Use Taylor's polynomial of degree two about c= - 4 to estimate the value of…

A: Solved below

Q: 1 Consider the function defined by f(x) over [-1, 1]. SET-UP the Lagrange 1+ 12x2 polynomial…

A: Lagrange's Interpolation formula can be defined as:…

Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

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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: According to the Table below calculate the function value at x = 2: a) by using Linear Interpolation…

A: The given table of values is

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

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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: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

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: 1 2. Consider the function defined by f(x) = over [-1, 1]. SET-UP the Lagrange %3D 1+ 12x²…

A: Given function is fx=11+12x2 over interval -1, 1. Now 11 equally spaced nodes on -1, 1 are -1, -0.8,…

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: To approximate f'(xo), suppose first that ro e (a, b), where fe C (a, b), and that x1 = xo + h for…

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Q: Find the dérivative of the function: f(x)=In(e^x-13x)

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Q: The Maclaurin polynomial of degree 4 for the function f(x) = cos(x) is %3D

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Q: Joyce wants to approximate the value of f(a) for some a  [-0.2,0.2] notation. accurate to one…

A: Given  And centred at a=0

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

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Q: Let f(x) = e* for 0 < x<1 a. Approximate f(0.25) using linear interpolation with xo = 0 and x1 = 0.…

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Q: 1. For the given functions f(x), let xo 0, x= 0.6, and xy = 0.9. Construct interpolation polynomials…

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Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: Let f(x) = cos(E) and P(x) be the interpolation polynomial of degree at most 3 which agrees with…

A: Neville’s method generates Lagrange’s approximations recursively. In Neville’s method, we denote…

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: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

Q: Given the relation f(x) = 2x^2 + 1 - e^x a. Using the convert equation x = √( e^x -1)/ 2, find the…

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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 f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

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Q: 1. For the given functions f (x), let xo = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation…

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Q: Suppose that only the points (x,y), j = 1 ... 16, that lie on the graph y = f(x) of a function f(x)…

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