1 2 5 7 8 f(x) 3 6 19 99 291 444 Calculate f(4) using Newton's interpolating polynomials of order 1 through 4. Choose your base to attain good accuracy. What do your results indicate regarding the order of the polynomial used to generate the data in the table?

Q: 1- Use Neville's method to obtain the approximations for Lagrange interpolating polynomials of…

A: Use the formula of Neville's method for degrees one, two and three. Substitute the values from the…

Q: 1. Given the data 1 2 5 7 8 f(x) 3 6 19 99 291 444 Calculate f(4) using Newton's Interpolating…

A: The given data is - x y=f(x) 1 3 2 6 3 19 5 99 7 291 8 444 We have to find the…

Q: A. FIND THE INTERPOLATING POLYNOMIALS OF ORDER 1 to 4 USING NEWTON'S DIVIDED DIFFERENCE (USE EXCEL)…

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Q: a) Calculate f(3.4) using Newton's interpolating polynomials of order 1, 2 and 3. All numeric values…

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Q: (10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of…

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Q: Formulate the required Newton's form of the interpolating polynomial for the given function using…

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Q: a) Let P3(x) (classical) be the interpolating polynomial for the data given in Table 1. Find y if…

A: Note: Since you have posted multiple questions, according to our policy, we are only supposed to…

Q: tion 10 Jsing Newton's backward difference polynomial of degree 2, for the below data, approximation…

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Q: Formulate the required Newton's form of the interpolating polynomial for the given function using…

A: The second-order Newton interpolating polynomial  formula based on known points and its resulting…

Q: 2. (a) Using Lagrange Inverse Interpolation method, find the value of x when y= 29 for the following…

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Q: Find the newton polynomial formula for the given data 4 6 10 f(x) 1 3 8 16 Select one: 3x² – 22x +36…

A: Newton's divided difference formula for n points can be defined as…

Q: Approximate  f′(2)f′(2) using the given data f(0)=−8,f(0)=−8, f(1)=−7,f(1)=−7, f(2)=0,f(2)=0,  and…

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Q: 3. Use Newton the forward-difference formula to construct interpolating polynomials of degree one,…

A: For the given data points, the interpolating polynomial is the lowest degree polynomial that passes…

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

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Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

A: The given data is f(0)=2 ,f(1)=3, f(2)=12, f(3)=41.

Q: Q.No.7 From the following table, obtain f(x) as a polynomial in powers of (x-5) using Newton's…

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Q: 1. Use the data given below to estimate f(3) by X 1 4 f(x) 62 Constructing: a. Linear polynomial b.…

A: Please find attachment below

Q: 3. Given the following data: 0. 3. 4 6. f(x) 7 11 28 63 89 (a) Complete a Divided Difference Table…

A: Given data are x 0 2 3 4 6 f(x) 7 11 28 63 89 Newton divide difference table for the given…

Q: 2. (a) Find the unique polynomial of degree 2 or less such that f(0) = 1, f(1) = 3, f(3) = 55 using…

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Q: 1- The Newton's divided interpolating polynomial on x, = X;-1 + 0.25 , Vi= 1,2,3 , X, = 0 given by…

A: We have given Newton divided interpolating polynomial for f(x) In P3(x) we just need to put x=0.75…

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: 2- Use the Newton backward-difference formula to construct interpolating polynomials of degree one,…

A: formula for newton backward difference is  y r = y+ r∆y+ rr+12!∆2y _...   where r =x-xnh

Q: 3 4 6. 0. f(x) 7 11 28 63 89 (a) Complete a Divided Difference Table for this data. (b) Construct a…

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Q: Q2: Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find…

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Q: Based on the given function below x0 = 0.15, x1 = 0.25, x2 = 0.30 and x3 = 0.45 Using the…

A: As we can see points are not equidistance so we will use the divided difference method. Formula for…

Q: 1.6 2 2.5 3.2 4 4.5 f(x) 2 8 14 15 8 2 a) Calculate f (2.8) using Newton's interpolating polynomials…

A: We have to numerically find the value of f(2.8) using the Newton's interpolation method with order…

Q: 2. Evaluate the Newton polynomial and find f (3) Xị -2 1 41 f (x) -15 1 -3 -7

A: xi f(xi) -2 -15 0 1 1 -3 2 -7 5 41

Q: 1- The Newton's divided interpolating polynomial on x, = x,-1 + 0.25 , Vi= 1,2,3 , xo = 0 given by…

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Q: 4) The following data are given. Firstly, write the general formula of the third-order Newton's…

A: First, write the general formula in terms of x0 , x1 , x2 , x3 . Then make the divided difference…

Q: 2. Construct a polynomial for the data given below, using Newton's divided difference formula. Find…

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Q: :Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find…

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Q: 2. The voltage drop V across a resistor for a number of different values of current i is shown in…

A: (1) Given i V Vi , Vj Vi , Vj , Vk 0.75 -0.6         0.7-(-0.6)1.25-0.75 = 2.6   1.25 0.7…

Q: 1. Given the following data: 3 4. 6. f (x) 7 11 28 63 89 (a) Complete a Divided Difference Table for…

A: We are given the following data : x 0 2 3 4 6 f(x) 7 11 28 63 89 We have to compute: (a) A…

Q: 1. Determine the fourth-order polynomial in Newton and Lagrange form that passes through the points…

A: Given,

Q: B. For the following experimental results x: 2 3 5 6. 7 y: -3 0 1 0 -2 Use Newton's divided…

A: The value of the table for x and y x 2 3 5 6 7 y -3 0 1 0 -2 Numerical divided differences…

Q: The observed data are given below -10 -5.2 5.4 15 30 20 45 f(3 12.6 50.2 60 a)Use the divided…

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Q: a) Use the Lagrange estimate of the residual term to find the degree of the Maclaurin polynomial…

A: The Maclaurin series is used to approximate the value of the difficult terms. The series value is…

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). 1 4 1 -1 1 -1 I

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Q: Q3. Let f(x) = x + 2 In(x + 1). (а)( (b) (c) ( | Hint: Use only 5-decimal digits in all your…

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Q: Calculate f (3.4) using Newton.s interpolating polynomials of order 1 through 3 and estimate the…

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Q: 1 Consider the function f(x) , x > 0. x + 2 (a) Find the interpolating polynomial P2(x) that agrees…

A: Substitute 0, 1 and 2 for x in the function fx=1x+2, and tabulate the values of x and f(x).…

Q: 1. Find the Lagrange form of the interpolating polynomial for the following table of values: *| 1/3…

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Q: Exercise: Newton's Divided Difference Method (a) Construct a divided difference table from the…

A: We use newton's forward and backward divided difference formula

Q: Find the newton polynomial formula for the given data 6 10 f(x) 3 16 Select one: 3x² – 22x – 36 y =…

A: We have to find the Newton's divided difference interpolation formula for the given table of values…

Q: (a) Find the Taylor polynomial of degree 2 of the given function at a = 2. 1 f(x) = P(x) =| (b) Find…

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Q: 8. In Newton-cotes formula, if f(x) is interpolated at equally spaced nodes by a polynomial of…

A: To find- In Newton-Cotes formula, if fx is interpolated at equally spaced nodes by a polynomial of…

Q: Table 1 Temperature as a function of resistance. R (ohm) T (°C) 1101.0 11.3 911.3 20.131 636.0…

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Q: 2. Given these data X 1 3 7 f(x) 3 19 99 291 Estimate using Newton's interpolating polynomial and…

A: x fx fxi, xi+1 fxi, xi+1,xi+2 fxi, xi+1,xi+2, xi+3 fxi, xi+1,xi+2, xi+3, xi+4 1 3             3…

Q: 1- Using Newton's backward difference formula, construct an interpolating polynomial of degree 3 for…

A: When the value of function at certain equally spaced points is known then the Newton's backward…