VII. Write a polynomial f(x) that meets the given conditions. 11.) Degree 3 polynomial with zeros 2,- 3i, and 3i.

Q: Suppose that f(x) is a polynomial of degree 3. Show that f(x) is its own clamped cubic spline, but…

A: The nth degree polynomial can be represented as Pn=a0+a1x+a2x2+…anxn. It is known that ddxxn=nxn-1.

Q: Interpolate the function f(x) = ev3 on [-1, 1] with a second degree polynomial by using the zeros of…

A:

Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

A: Let the polynomial is  fx=αx-15x--23x-4=αx-15x+23x-4=α5x-153x+22x-4 Coefficient will be integer if α…

Q: 2. Find a Taylor polynomial of degree N=5 for f(x) xpanded about xo=0.

A: Formula

Q: 2) Use the first 3 terms of the Taylor polynomial (i.e., the second degree Taylor polynomial) for…

A: The Taylor polynomial of degree 2 formula is: P2(x)=f(a)+f'(a)1!(x-a)+f''(a)2!(x-a)2 Here,…

Q: Find the Maclaunin polynomial of degree 3 for the fuction. - ge

A: The given function is:fx=e-9xTo find the Maclaurin polynomial.

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Write a 4th degree Maclaurin polynomial for f(x) = e2x centered at x = 0. %3D

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Q: Let g (x, y) = 9 sin(xy) – 11x² In(y) + 4. Find the degree 2 polynomial, p, which best approximates…

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Q: Lat R= 7@7. Show that %3D the polynomial (1,0)x in has in finitely R[x] many roots in R

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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: 2) FIND THE TAYLOR POLYNOMIAL 13 (x) foR THE FUNCTEON f CENTERED AT THE NUMBIER a . TOU ON -4x flx=…

A: f(x)=xe-4x, centre at a, where a=0

Q: IV. Write a polynomial f(x) that satisfies the given conditions. 7.) Polynomial of lowest degree…

A:

Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

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Q: What is the nth Taylor polynomial of a function f(x) at x=c?

A:

Q: 2.33 Let p(r) = x4 + x³ -- 2x2 + x + 1. Prove that the polynomial equation p(x) = 0 has a root in…

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Q: 4- By using Lagrange polynomial the vahue of f'(3) from the following table is 52 2 4 112 f(x) -2 F…

A:

Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

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Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: 1) Let f(x) = e2* Find 3rd Maclaurin Polynomial for f(x)

A: Given f(x)=e2x To find the third order maclaurins polynomial

Q: 13) Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given…

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Q: Q2 /| Find a cubic polynomial of x (5, 147). given points (0, 2), (1, 3), (2, 12),

A: Newton's divided differences interpolation

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: (B): For the function f(x) sinx, let x, = 0, x1 = 0.6, x2 0.9.Construct Lagrange polynomial %3D…

A: Given fx=sinx, x0=0, x1=0.6, x2=0.9. The lagrange polynomial interpolation of order 2 for a function…

Q: Determine the third Taylor polynomial of the function at x = 0. fox) = 3 X+3 01 1 3 81 01.1 x3 81 x+…

A: Given: fx = 1x+3 To evaluate: Third Taylor polynomial at x=0 In the third degree of Taylor…

Q: Find the second-degree Taylor polynomial for f(x) = 4x² – 8x + 8 about æ = 0. %3D P2(x) = What do…

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Q: 1. Find the zero's (aka roots) of the polynomial function and state the multiplicity of each (d)…

A: To find the zero with its multiplicityd) x+52x-4x+1e) x+53x-4x+1f) xx-1x+1

Q: 7. a) Use the appropriate Lagrange interpolating polynomial of degree two P,(x) to approximate…

A: Given f0.1=0.665, f0.2=0.8, f0.3=1.8, f0.4=0.25

Q: 12. The second-degree Maclaurin polynomial for f(x)=vx+9 is 3+ x² If this 6 108 polynomial is used…

A: The Maclaurin polynomial for f(x)=x+9is 3+x6-x2108 To approximate 8, substitute -1 for x in the…

Q: 5. a) Find the second Taylor's polynomial P2(x) approximating the function f(x) = x + In (1+ x)…

A: Consider the given function. fx=x+ln1+x (a) We have to find the second-order Taylor polynomial about…

Q: 2. y = cos ( 2x ) at x = [0,r] with four equally spaced points. %3D

A: The interpolation techniques are used to establish the functional relationship between any two…

Q: Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Given,  f(x)=ex

Q: Construct lagranges interpolating polynomial of atmost degreee2 to approximate f(2.3) from the table…

A:

Q: 35. Verify that Tn (x) = 1+ x + x? + ..+ x" is the nth Maclaurin polynomial of f(x) = 1/(1 – x).…

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Q: 9. Estimate the error in approximating sin(0.5) by using the fifth-degree Maclaurin polynomial by…

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Q: Polynomial of lowest degree with zeros of -2 (multiplicity 2) and 3 (multiplicity 2) and with f (0)…

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Q: Determine all Taylor polynomials for f(x) = x^2 + 2x + 1 atx = 0.

A: Given: fx=x2+2x+1 x0=0

Q: 4. Find The coefficient of the x’term in the Maclaurin polynomial for sin(2x)

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Q: A Cubic polynomial is dlefined by the table 3. 10 tind the equation of the palyinmal Using Lagrange…

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

A: The solution is given below in the next step:

Q: 1)Find the fourth degree Maclaurin polynomial for the function. f (x) = e3z

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Q: 2. Let g(x) = evcos +, Approximate the value of g(0.2) using the second degree Maclaurin polynomial…

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Q: 2) Find the 3€ Tayler polynomial P,(x) fix) = Sinx at X= -½. 3) Using B,(x) from 2), estimake sin…

A: The formula for taylor series is     where f (k) (a)  is kth derivative of f at given point a.

Q: find the Taylor polynomial of degree "n" about x=1 for the function f(x)=1/x

A: We have given,

Q: Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.…

A: here we us e the linear factors for the zeroes given see below the calculation

Q: Let g (x, y) = 9 sin(xy) – 11x² In(y) + 4. Find the degree 2 polynomial, p, which best approximates…

A: Given: g(x, y) = 9sin(xy) -11x²ln(y) +4 To find: Taylor Polynomial of 2nd degree   Dear student,…

Q: is a polynomial O has repeated roots at x = 0 O has a slope equal to zero at x = 0 O is always…

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Q: 6. Find the third degree Maclaurin polynomial for f(x) = cot-(x) and use this to approximate…

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Q: To find an nth Lagrange interpolation polynomial p(x) we need n distinct numbers and their values in…

A: To find an nth Lagrange interpolation polynomial p(x) we need n distinct nbers and their values in…

Q: 1. Use the numbers x, =1 , x, = 2 and x, = 3 to find the second Lagrange interpolating polynomial…

A: We have x0=1, x1=2, x2=3 The polynomial is fx=x-2=1x2 Therefore,…