Find the Taylor polynomial of order 3 generated by f at a. f(x) = In (x+ 1), a = 4 X- 4 O A. P3(x)= In 3 – (x- 4)? )3 +. 3. 18 81 X- 4 O B. Pa(x) = In 5+ x– 4 (X-4) (X – 4)° (x – 4) +. 50 375 x- 4 (x-4) (x- 4)³ Oc. P3(x)= In 3+ 3 18 81 x-4 (x-4) (x- 4)° +.

Q: 1. Fill in the table below with information about each of the following polynomi Polynomial Degree…

A: Given that:

Q: Let p(x) be a polynomial that is divisible by (x-a)n where n∈ N and n >= 2. Prove that p'(x) is…

A: Here, given that the polynomial p(x) is divisible by (x-a)n. So, p(x)=(x-a)nq(x)...(1) Where, q(x)…

Q: ose P(x) is a polynomial satisfying - P(5) = - 5 - P'(5) = - 305 - P''(5) = – 156 - P(3) (5) = - 414…

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Determine the third Taylor polynomial of the function at x = a. f(x) = x 2 + x+1, a = 4

A:

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Q: Calculate the Taylor polynomials T, and T3 centered at a = 3 for the function f(x) = x4 – 5x. (Use…

A:

Q: 39.. Find the Taylor polynomials (centred at zero) of degrees (a) 2, (b) 4, (c) 6, (d) 8. 1 f(x) =…

A: We know that Taylor Expansion : f(x)=11+x=1-x+x2-x3+x4-.........∞.

Q: 3. Find the fourth degree Taylor polynomial centered at C=8 for the function. f(x) =ln x In 8-x-8)…

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Q: Also, our definition of the first 4 Legendre polynomials is: 1 Po(x) V2 P1 (x) = V5/2 (1 – 312)…

A:

Q: 'hich of the following is the 3rd degree polynomial expansion of e" at a = 3? A. 0.453x³ + 8.34x –…

A: Let's find.

Q: 1. P(x) = px' –8x² +qx +2 is divisible by 2x-1 and when divided by x-1, the remainder is 3, where p…

A:

Q: Given the three function below, which expression equals (co f o z)(x)? c(x) = 2" f (x) = V3x z(z) =…

A: We have to find

Q: LOW: Construct polynomia -) sinx in [0, 2π] interpolation in mentioned interval of the function

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: (8). Suppose that P(x) = x³ + 4x2 – 7x – 10 Find a polynomial Q(x) such that (x – 2)Q(x) = P(x)…

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Q: A6. Using Taylor's expansion, expand the polynomial f(r) = 2r - 13r + 28r - 11 in the form f(r) = ao…

A:

Q: Let P(x)=20x*-7x3 be the Lagrange interpolating polynomial that approximates a function f over the…

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Q: 3. Subtract Expressed as a single fraction, x- 1 is equivalent to x-2 А. x(x – 1) В. x(x – 1) x+2 3x…

A:

Q: 4. a) Find the second Taylor's polynomial P2(x) approximating the function f (x) = e2* + cosx about…

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Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

A:

Q: (c) (i) Express the decimal 9.999 in the form where a, b € Z.

A:

Q: The Taylor polynomial of the function f(x)= e* up to order 3 about X = 0 is given by 1- x+x²- 6 a O…

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Q: Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In|4x +31)], transform it to z. A.…

A:

Q: If you use the second Taylor polynomial of f(x)=√x centered at x = 1 to estimate √1.1 as √1.1=1+…

A: We have to find the error by the Taylor's series method.

Q: 6. (x – 1

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Q: Determine the irreducible polynomial for 15 over each of the following (c) a = /3 fields (i). Q (ii)…

A:

Q: B Find the Taylor polynomials p4 and p5 centered at a = 6 for f(x) = 4 cos (x).

A:

Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

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A:

Q: Now suppose b +0. The characteristic polynomial of A is (a-X)(d-A)-b² = x² − (a+d)λ + ad-b². From…

A: Please find the answer below

Q: Find the 3rd degree Taylor polynomial T3 (x) centered at a 2 for the function f(x) = e"/5 e2/5 (x-…

A:

Q: Question 2 Find the Taylor polynomial P5(x) centered at x = 0 for the function f(x) = 5x² – 3…

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Q: The Rodrigues Formulae for the Legendre Polynomial is 1 d' P:(x) = 2'4 dr (x-1)- Using this formula…

A: The Rodrigues Formula for the Legendre polynomial is Ptx=12tt!dtdxtx2-1t Now, we have to find the…

Q: (27) Let X = P(2) and )E(5-5x) finc

A: Given X≈Pλ That is, EX=λ

Q: e truncation error in approximating e by o is ect one: a. Lk-5 k! b. 5! + 120

A:

Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

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Q: Give an example of a polynomial of degree 4.

A: In Mathematics, a polynomial is an expression consisting of variables and coefficients that involves…