Q) Approximate f (0.3) using Divided difference method to construct polynomial of degree one, two, three for the following data (x) 1.00000 0.0 0.2 1.22140 1.49182 0.4 0.6 1.82212

Q: 10. Using the given data, estimate the value of f(x) at x = 3.2 by defining a 2nd-order direct fit…

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Q: •Use the Newton backward-difference fomula to construct interpolating polynomials of degree one,…

A: In the given question, the concept of Newton's backward-difference formula is applied.…

Q: Interpolate the following data to estimate the pressure at 1.15 minutes using 2nd order polynomial…

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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: please answer the questions in the images. thank you.

A: Given.

Q: Q-when fitting the data shown in the table with a second order polynomial Y=a+bx+cx? The value of a…

A: Make a table for the given data as follows                x y x2 x3 x4 xy x2y 1.2 1.5403 1.44…

Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

A: Solution : y=f(x) 1. Lagrange's Interpolation formula is,…

Q: Use Divided difference method to construct a second degree polynomial P2(x) to approximate f(x) = e…

A: Newton's Divided Difference Interpolation formula is…

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

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Q: The divided difference table above is for the data: X are: f(x) (4) ao = -0.2 0.0 0.1 a) Do not…

A: The divided difference table is used to determine the interpolating polynomial using the divided…

Q: Let f(x) = e^x. Find the polynomial P2(x) of degree at most 2 such that P2(1) = f(1), P2(2) = f(2),…

A: We have to find the polynomial of degree 2 for the function fx=ex using the divided difference…

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: Q6) Fit a second order polynomial to the following data. Also estimate the value of y at x=1.25,…

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Q: A bullet is fired upward with its velocity against time given in the table below: Time t in seconds…

A: The given problem is to find the value of velocity of time t=16 from the given data using Lagrange…

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

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Q: Using the provided data, find the interpolated value of f(x) when x = 3 using Newton's Divided…

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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: 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: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

A: Given: x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12 To find: Construct the…

Q: Given these data X 1 2 3 f(x) 3 6 19 99 Estimate f(2.5) and f(4), (a) using an interpolating…

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Q: 2. Consider the following data values 1.5 2 2.5 3 f(x) 8 14 18 Find the value Of f(x) at x= 2.65…

A: Newton's divided difference interpolation formula is a interpolation technique used when the…

Q: Interpolate the following data to estimate the pressure at 6 minutes using 2nd order polynomial (By…

A: Lagrange's interpolation formula for the second-order polynomial is . The points for the polynomial…

Q: Approximate f(0.5) employing Lagrange interpolation polynomial with the nodes xo=0, x1=0.6, x2=0.9…

A: First, find the values of y that correspond to x. For this substitute the values of x in f(x).  x…

Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using xo =…

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Q: Q5. Use Newton's interpolatory divided- difference formula to construct interpolatin polynomial of…

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Q: Obtain the Lagrange interpolating polynomial using all the data points below: x 0.5 1.0 1.5 2.0 2.5…

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Q: Consider the data below: X 200 240 300 350 f(x) 1100 980 820 700 Approximate f(320) using Lagrange…

A: Given: The value of table for x and y x 200 240 300 350 y 1100 980 820 700 The objective is…

Q: 0.125 0.250 0.375 0.500 0.625 0.750 f(x) 0.79168 0.77334 0.74371 0.70413 0.65632 0.60228 1- Using…

A: Lagranges interpolation formula of order 3  with 6 points (x0,y0),(x1,y1),(x2,y2),(x3,y3),(x4,y4)and…

Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

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Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 0.4 0.8 1.2 1.6 2 Ly 0 0.25 1…

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Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using x, = 8,…

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Q: 2.Use the Newton interpolation polynomial to find f(0.05) based on the following data points {(-0,5,…

A: Given data is  {(-0.5,0.97939),(0.15,4.72743),(0.5,13.69506),(1,61.25661)} we have to find the value…

Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

A: A table with values x and y is given below, x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625…

Q: 5) Find the velocity of rocket by using Gregory-Newton interpolation polynomial at t=260 sec. time…

A: Consider the given table. We have to find the velocityt=260 sec Since, t=260 sec is near to the…

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

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Q: T (F) H (btu/lb) 800 1000 1200 1400 1600 1303.6 1458.4 1585.3 1706.1 1826.1

A: We can solve this by using Lagrange's interpolating polynomials of degree 2

Q: Interpolate the following data to estimate the pressure at 1.5 minutes using 2nd order polynomial…

A: The order polynomial approximation of f(x) using Lagrange Interpolation is  .

Q: 2)tind the third degree Taylor polynomial Is (x) centered at a= I forr the function f (x)= 2

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Q: Q// Fit a second-order polynomial to the :following data Y 7 11 7 5 2 10 4 7 2 11 11 3 y = 8.440138…

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Q: Given that f(x) = x³ – 0.3x² − 8.56x +8.448. - Use polynomial interpolation to compute f'(x) and…

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Q: a) For the given function (x) = V1 – x , let xo = 0, x1 = 0.4 and x2 = 0.7. Construct a agrange's…

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Q: Q2: Construct the second order Lagrange interpolation polynomial for the function f (x) = In(x + 1)…

A: Given table

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: Consider approximating the function f(x) = e¯1.9€ on the interval (0,0.46] by linear interpolation…

A: Given, f(x)=e-1.9x   Theorem:Let P1(x) be the linear polynomial that interpolates f(x) at x1 and x2.…

Q: Interpolate the following data to estimate the pressure at 7 minutes using 2nd order polynomial (By…

A: Given,

Q: 4. Use the Newton's Interpolating Polynomial to determine y at x = 3.5 to the best possible…

A: Newton's Divided Difference Interpolation formula can be defined as:…

Q: Q3. Interpolate the following data to estimate the pressure at 1.05 minutes using 2nd order…

A: Interpolating polynomial is an approximate polynomial that passes through the given data points.…

Q: Q) Approximate f (0.25) using Hermite interpolating polynomial to construct an approximation…

A: Hermite Interpolation Formula is H(x)=∑ui(x)*yi+∑vi(x)*yi' where, ui(x)=[1-2(x-xi)Ii'(xi)][Ii(x)]2…

Q: The following data shows the height function of a hill a a distance x from a reference. Form a cubic…

A: Given Information: Consider the given data: x h 0 4 1 5 2 10 3 17 4 21 5 16 6 11…

Q: Fit a second order polynomial to the following data i 1 2 0 0.4 0.8 0 0.25 1 5 6 1.6 2 4 6.25 3 4 X…

A: Let a second degree polynomial that needed to be fitted to the given data be a0+a1x+a2x2=y-----(1)…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.