F(X) 2 2 4 7 29 12 64 27 111

Q: Let P(x) be the Lagrange interpolating polynomial of the function f(x) = In(x-2) at the nodes x, =…

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Q: 2. The following data shows the height function of a hill a a distance x from a reference. Form a…

A: Data is given for x and h We have to calculate cubic equation and standard deviation for mentioned…

Q: Regress the data of strain vs strain to a second order polynomial Table 1. Strain Stress %) (MPa)…

A: The general quadratic function is defined by the equation, f(x)=a+bx+cx2. Here, x is the independent…

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

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Q: Q.5: For the given data; x f(x) 1 3 2 6 3 19 5 99 7 291 8 444 Calculate f(4) and f (2.5) using third…

A: Let the given data be x0,y0, x1,y1, ..., xn,yn. To obtain the n-th order Lagrange interpolating…

Q: Using the data of the table below, apply Gregory-Newton's backward divided differences to…

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Q: Let P(x) be the Lagrange interpolating polynomial of the function Ín(x=2) f(x) at the nodes x, = 3,…

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Q: Using the data of the table below, apply Gregory-Newton's backward divided differences to…

A: solution :The given date is below mentionedHere all as de points are equally placed at the values of…

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

A: Introduction: The Lagrange interpolating polynomial is a basic interpolating polynomial that fits…

Q: DETERMINE THE VALUE OF F(5) FOR A GIVEN SET OF DATA BELOW USING THE STATED METHOD OF INTEPROLATION:…

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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: Find Lagrange interpolation polynomial P(x) which agrees with the following data and obtain a 1…

A: The Lagrange's interpolation polynomial for a function, y=f(x) that passes through the points x0,y0…

Q: Consider the table below to approximate f(21) using the first Lagrange interpolating polynomial…

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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: Construct the Lagrange interpolating polynomial L3(x) = yolo(x) + yılı(x) + yzl2(x) + yzl3(x), for…

A: Legranges interpolation

Q: Let P(x) be the Lagrange interpolating polynomial of f(x)%3= 3x +3 at the points Xg 0: x 1 and x; =…

A: 1/15 is the answer.

Q: X 1 4 7 9 11 f(x) 12 -23 -15 33 -13

A: The given set of data is                           x f(x) 1 12 4 -23 7 -15 9 33 11 -13…

Q: The function f(x) = 1/(x+1) is given. Using the points x0 =0, x1 =0.3, x2 =0.4, x3 =0.5; a) Write…

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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: 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: 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: 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: Let P2(x) be the interpolating polynomial for f(x) at xo = 0.5, x1 = 1.2, and x2 = 2. Find a bound…

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Q: Determine the 4th degree polynomial for the given set of data(x.y). 1. 1.3 2.4 3.7 3.8 5.1 y -6.3…

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Q: Q3 Consider the following tabulated data for the vapor pressure P (mm Hg) of water as a function of…

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

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Q: Use Newton's interpolating polynomial to determine y at x = 4 to the best possible accuracy x 3 5.25…

A: Given: x 3 5 2 6 1 y=fx 5.25 19.55 4 36 4.65 To find: y at x=4 using Newton's interpolating…

Q: (() A polynomial f(x) of low degree is tabulated as follows: -3 -2 |-1|0|1 23 4 5 6 f(x) – 30 | –12…

A: Suppose we wish to find the zeros of f(x) =  . Setting f(x) = 0 results in the polynomial equation…

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: (a) Construct a second degree Lagrange interpolating polynomial for f(x) = ! at the nodes x1 = 2, at…

A: The Langrange's interpolation method can be used to calculate the polynomial approximation for the…

Q: Consider the function f(x) = x³. Construct the Lagrange interpolation polynomial which interpolates…

A: We have to find the Lagrange's interpolation polynomial of the function fx=x3 using the given values…

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: Construct the Lagrange interpolating polynomial for the following data set 0.1 0 0.2 0.4 X f(x) 0.74…

A: We have to solve given problems:

Q: Let f(x)=√x-x² and P2(x) be the interpolation polynomial on x=0, x, and x = 1. Find the largest…

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Q: By using Lagrange's interpolation polynomial of order 1 through 3. Calculate f(3.5) from the…

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Q: Consider the function f(x) = x. Construct the Lagrange interpolation polynomial which interpolates…

A: It is given that fx=x3. We have to construct the polynomial using the Lagrange's interpolation…

Q: Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5, X2 =4…

A: Find second order Lagrange interpolation polynomial

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

A: Given table

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

A: Given,

Q: 2. Let f(x)=e". Find 4th-order Lagrange interpolation polynomial P4(x) using the nodes -1, -1/2, 0,…

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Q: 1 2 3 4 5 6 f(x) 3 6 11 30 75 158 291 f(x) = f'(x) = f" (ε) f"'(x) = f(0.5) f'(0.5) f"(0.5)

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Q: Q3. Use Lagrange interpolating polynomials of order а) 1 b) 2 c) 3 to determine y at x=1.32 for the…

A: Let  x0=1.20x1=1.25x2=1.30x3=1.35fx0=0.1823fx1=0.2231fx2=0.2624fx3=0.3001 The, Lagrange…

Q: Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute…

A: The given table is  x 8 9 9.5 11 f(x) 2.07944 2.19722 2.25129 2.39789 The objective is to…

Q: Consider the interpolation data given below: x|1|1/2|3 y 3-10 2 The interpolating polynomial…

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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)…

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

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