[E] The following values are obtained from a polynomial of degree three. 8, 3, 10, 40, 108, 223, 398, 648, 976, 1403, Four values (a, b, c, d) from this list are erroneous! With the help of a difference table, identify the values in error (arrange in ascending order a

Q: Determine the smallest degree of the Madlaurin polynomial required for the error in the…

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Q: Use this interpolating polynomial for the data points f(x) 1 0-368 1-2 0-301 1-3 0-273 1.5 0-223 To…

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Q: [E] The following values are obtained from a polynomial of degree three. 8,3, 10, 40, 108, 223, 398,…

A: Three degree of  polynomial equation is        y=ax3+bx2+cx+d       where a,b,c,d  are constant.

Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: We have to approximate the function at the given value of x: fx=e4x,      f14 To find f14 we need to…

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

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Q: If a polynomial f(x) when divided by (x – a) gives a remainder r1, and when divided by ( – b) gives…

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Q: In the given question as follows , find the nth Maclaurin polynomial for the function:- f (x) =…

A: Maclaurin series is a special case of Taylor's series where the specific point on which the series…

Q: Find the nth Maclaurin polynomial for the function. 4x - 1 f(x) = n = 4 P4(x) =

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Q: 22/By using Newton's backward difference formula, construct an interpolating polynomial from the…

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Q: Which of the following polynomials has a remainder of 1 when divided by x + 2, x + 3 and x + 5? x³ +…

A: We have to find the polynomial

Q: Fit a second-order polynomial to the data in the kollowing daha- 0|12/31415 yi 2.17.713.6|272 40.9…

A: The objective is to find a second order polynomial and to find the standard error.

Q: The following polynomial represents the number of major hurricanes that struck the U.S. x decades…

A: Note: According to the guidelines only one question will be answered at one time please upload other…

Q: Find the nth Maclaurin polynomial for the function. 4x - 3 f(x) n = 4 X + 1 P4(x) =

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Q: For the following, find the Maclaurin polynomial of degree n. (a) xe", where n = 3 (b) vsin(x),…

A: The answer is given below:

Q: The upward velocity of a rocket is given as a function of time in Velocity as a function of time. t…

A: Consider a set of n+1 data points. For those data points fit a polynomial of order n as…

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: 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: Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers…

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Q: A car traveling along a straight road is clocked at a number of points. The data from the…

A: Now apply Spline interpolation conditions with clamped boundary conditions to get the following…

Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 6. X 0.4 0.8 1.2 1.6 y 00.25 1…

A: In the given question we have to define a second order polynomial to a givendata  i 1 2 3 4 5 6…

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: 14. Evaluate this cubic polynomial for x = 1.32, using both rounding and chopping to three digits at…

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Q: Change the following data, such that the data follows a certain fourth-degree polynomial. X: -2 -1 0…

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

Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) = n = 4 x + 1 P4(x) =

A: A Maclaurin polynomial of nth order  for the function f(x) is               f(x) = ∑n=0∞fn(0)n!xn,…

Q: Divide the polynomial f (x) = to 6 x ^ 3 + 4 x ^ 2 - x + 5 by x ^ 3 - 3 x + 2

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Q: 2. Evaluate the polynomial: y = x° – 7x + 8x – 0.35 at x = 1.37. Use 3-digit arithmetic with…

A: Explanation Given polynomial is  y = x3-7x2+8x-0.35 we have to evaluate the given polynomial at…

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: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

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 a function  f , the Newton divided-difference formula gives the interpolating polynomial P3(x)…

A: Given data: The given interpolating polynomial is P3(x)=1+4x+4x(x-0.25)+(16/3)x(x-0.25)(x-0.5). On…

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: Q4) Fit a second order polynomial to the following data 5 6 1.2 1.6 4 6.25 i 1 3 4 0 0.4 | 0.8 0…

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Q: 2.3. Approximate fl1895) vising an interpolacting polynomial of degree & using Netu tons.…

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Q: = -5. Let p2(x) be the interpolating polynomial of f(x) at xo = Then, the error term in…

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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: Q// Fit a second-order polynomial to the following data: Y 9 8 3 7 9 11 9 6 1 7 1 3 10 9. 1 a. y =…

A: Given x y 9 8 0 3 7 9 11 9 6 1 0 0 0 7 1 3 8 10 9 1

Q: The polynomial that passes through the following x.y data x18 22 24 ? 25123 is given by…

A: Given that the polynomial passes through the x, y data                                 x 18 22 24…

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X01 4 6 y 1 -1 1 -1

A: Newton's divided differences

Q: Fit a second order polynomial to the following data 1 2 4 0.5 1.0 1.5 2.0 2.5 0.25 1.0 2.25 4.0 6.25

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

A: Percentage  of lead in the alloy (p) 50 60 70 80 Melting Point (Q0 C) 205 225 248 274 to find…

Q: If a polynomial f(x) when divided by (x - a) gives a remainder r₁, and when divided by (x - b) gives…

A: Given that fx is divided by x-a, we get remainder r1, so there exist a polynomial qx such that…

Q: By using L(x)%3D1and L(x)= 1-x in Lagure polynomials, calculate the value of

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Q: Find a formula for the n-th term of the Maclaurin polynomial for f(x) = 1+ x

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Q: 5.0 F10 10 -10

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

A:

Q: Find the nth Maclaurin polynomial for the function. 5x - 4 f(x): n = 4 x +1 P4(x) =

A:

Q: Q4) Fit a second order polynomial to the following data 1 2 3 4 5 X 0.4 0.8 1.2 1.6 Ly 0 0.25 1 2.25…

A: Equation of 2nd degree polynomial

Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) n = 4 x + 1 P4(x) = =

A: The function is  f(x)=4x-5x+1

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)…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.