Q5. Use Newton's interpolatory divided- difference formula to construct interpolatin polynomial of degree two for the following data and estimate f(8.5): S(8) =16.63553, (8.3)= 17.56492, (8.6) = 18.50515

Q: Assume that it costs that same company approximately C ( x ) =62,229+5,573x +0.033x 2 dollars to…

A: The given cost function is Cx=62,229+5,573x+0.033x2. It is known that, the average cost function can…

Q: Find the interpolating polynomial of the following points or functions using Newton's

A: Given: The points -2, 2, -1, -2, 1, 3 and 3, -3. To find: Interpolating polynomial.

Q: The following data define the sea-level concentration of dissolved oxygen for fresh water as a…

A: (a) Find the Newton's forward difference table.

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

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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…

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Q: Assume that it costs that same company approximately C() =67,822+4,195x+0.05x2 dollars to…

A: Given,          The cost function is Cx=67822+4195x+0.05x2 dollars to manufacture x of…

Q: With the given data points below, use every method in Polynomial Approximation and Interpolation to…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Q#7) compare the maximum error, average error, and RMS error for the f(x) = x³ - 3x to the data…

A: Introduction: In analysing the curve fitting for the given data points, the maximum error, the…

Q: Q2: Obtain the interpolation quadratic polynomial for the given data by using Newton forward…

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Q: 8. For the given function f(x) = v1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Construct an…

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Q: From the given data, identify f(4) using Newton's polynomial. (2,10), (3,15), (5,25), (8,40)

A: Explanation of the solution is given below....

Q: Given that f(0) = 1, f(1) = 3, f(3) = 55, find the unique polynomial of degree 2 or less, which fits…

A: Solution is given:

Q: Q2: The following tabulated data represent the influence values for vertical stress (12) under the…

A: From the given information. The given tabulated data is as follows.

Q: 32. The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

A: Newton's farword diffrence formula

Q: The following table shows data of velocity versus time that has been collected by an engineer in a…

A: The Lagrange's polynomial that passes through the points x0, y0, x1, y1, x2, y2 can be estimated…

Q: From a function, f(x), we obtain the following data points: (ri, f(x₂)) = {(-0.5, e³/2), (0, 1),…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

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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: The following data of the velocity of a body is given as a function of time Time (s) 0. 15 18 22 24…

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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' (2) using the given data f(0) = -8, f(1) = -7, f(2) = 0, and f(3) = 19 and the…

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

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Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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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: Use the fourth Maclaurin polynomial for f(x) = e" to estimate e0.5. Round your answer to four…

A: The Maclaurin series of ex is: ex=1+x+x22!+x33!+x44!+...

Q: [Q1] The following table shows the distance measured for a given time seconds in a car race Time (t)…

A: 1. We must find polynomial of the form S(t) = a + bt + ct2   Where, S represents the distance, a, b,…

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(5) = 147 and the…

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Q: Q1/ Use the polynomial that fits data shown by Newton divided difference ,and estimate

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Q: Approximate the following functions with a polynomial of order 3, calculate the absolute and…

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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: Consider the Cobb-Douglas Production function: P(L, K) = 13L04K©6 Find the total units of production…

A: Solution is given as below:

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: 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: 3. For the following data set, find the interpolating polynomial by the Lagrange's Method. 2. 4.

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Q: Construct a Lagrange interpolating polynomial to approximate u at the temperature of 38°C. Use your…

A: Given:                                     To find: Lagrange interpolating polynomial to…

Q: The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in the…

A:

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: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

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: A creep test is done at room temperature on a material on a metal alloy wire comprising of 30% Tin,…

A: Note: It is assumed that the quadratic equation asked in this case is of the form y=A0+A1x+A2x2.…

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

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Q: A car is moving with speed 60 m/s and acceleration 6 m/s? at a given instant. Using a second-degree…

A: To estimate how far the car moves in a second, given its speed is 6m/s and acceleration is 6m/s2 at…

Q: Consider the function f(x) = x³ + 2x + 5. 2. Estimate the root to eight significant digits using…

A: For an equation of the form f(x)=0 If xn is one of the root then next root xn+1 can be estimated by…