Which of the following polynomials in Z3 [x] is irreducible? (a) p (x) = x ^ 3 + x + 1 (b) p (x) = x ^ 4 + 1 (c) Factorize the polynomials that are not irreducible.

Q: Find the Taylor polynomial of order 3 centered at 0. 1 f(x) = 5-x x2 O P3(x) = +25 125 625 =-- x x2…

A: Rewrite the function as: fx=15-x      =15×11-x/5      =151-x5-1

Q: Find the Taylor polynomial of degree 2 centered at a=1 that approximates f(x)=ln(3x) P2(x)=

A: The general form of Taylor expansion of a function centered at a is, fx=∑n=0∞fnan!x-an The second…

Q: 7.) Explain why the eror term Rn(x) is ficitely bonded in every Tayler polynomial. Asnincreases, why…

A: Nothing

Q: Find an expression for the nth Maclaurin polynomial using sigma nota- tion for the function cosh x.

A: Suppose f has n derivatives at x=0 then nth Maclaurin polynomial of f is pn(x) where pn(x)=∑k=0n…

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

A: Formula

Q: Show that the Chebyshev polynomials have thefollowing properties: Tm(Tn(x)) = Tmn(x)

A:

Q: Are there any nonconstant polynomials in Z[x] that have multiplicativeinverses? Explain your answer

A: No, there is no any nonconstant polynomial in Z[x] that have multiplicative inverse.

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: Determine the third and fourth Taylor polynomials of x^3 + 3x - 1 at x = -1.

A: To determine the third and fourth Taylor polynomials of  x3+3x-1 at x=-1

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 5 (x- 5)4…

A:

Q: Find the coefficient of degree 2 in Taylor polynomial for f(x) = In (1+ rx) about x = = 1.

A: To find the coefficient of degree 2 in Taylor polynomial for the give function- f(x)=ln(1+rx) about…

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

A:

Q: Find ALL irreducible polynomials of degree 2 or 3 in Zr].

A: An irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the…

Q: ) Find the Taylor polynomial p2 for f(x) = at x = 2. x3

A:

Q: Find real zero of f(x) = x* – 2x³ – 4x² + 4x + 4 within TOL = 10-5 by following methods:

A: First, plot the curve for f(x). Use the graph to find a real zero as mentioned in the question.…

Q: Find the Taylor polynomial p5 for f(x) = 3 ln(x) at x = 1. Sorry, that's incorrect. Try again?

A:

Q: 13 - What is Taylor polynomial with order 3 generated by f(x) = x° + 3x² + 2x + 4 at x = 1.

A: The Taylor polynomial of order 3 is given as follows :

Q: Find the Taylor polynomial Tz(x) of f(x) = In x at x=

A: Given:

Q: Determine the nth Taylor polynomial of f(x) = 1/x at x = 1.

A: We know that the Taylor series expansion of a function f(x) is given as: ∑n=0∞fnan!x-an where fna is…

Q: Express p (x) = 1 + 2x -5x2 as a Taylor polynomial about a= 1

A:

Q: I am trying to find out if the polynomial 12x^4+8x^3+9x^2+4x+4 is reducible or irreducible over Q.…

A: The given polynomial is, 12x4+8x3+9x2+4x+4

Q: sin

A:

Q: Show that the Maclaurin polynomials for f (x) = ln(1 + x) are

A: The given function is fx=ln 1+x. fx=ln 1+x f0=0 f'x=11+x f'0=1 f''x=-11+x2 f''0=-1…

Q: List all the polynomials of degree 2 in Z2[x]. Which of these areequal as functions from Z2 to Z2?

A:

Q: Find the polynomial with thats has degree 3 and Zeros 2,-1 and 3

A: To find the polynomial with thats has degree 3 and Zeros 2, -1 and 3.

Q: 3. Use Lagrange interpolating polynomial of degree 4 to estimate f(1.9). 0.5 1.2 1.7 2.1 3.0 f(x) 1…

A:

Q: Find the Taylor polynomial of degree four for the function Ax) = x/4 at x = 1.

A: Taylor polynomial of degree 4 is given…

Q: 2) Find the third degree Taylor polynomial centered at c= for the function. 6 f(x) = sinx

A:

Q: Express p (x) = x3 as a Taylor polynomial about a = 1/2

A:

Q: (This is closely related to "Taylor polynomials" which appear at the end of 1st year calculus.)

A:

Q: The Taylor polynomial of degree 100 for the function ƒ about x = 3 is given by (x – 3)100 50! 2n…

A:

Q: The Taylor polynomial of degree 3 centered at x=0 of the function f defined by f(x)=sen(8x)+cos(9x?)…

A:

Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…

A: We have to show that,  the distinct polynomials x4+x  and x2+x in ℤ3x determine the same function…

Q: Find the Taylor polynomials of degree n = 2 for f(x) = ein centered at a =0. %3D

A: Given:        fx=esinx   A Taylor series is given by fx=∑k=0∞fkak!xk Here n=2, a=0…

Q: The 1st-degree Taylor polynomial of sin(x) is x. Select one: True False

A: We have to choose the given statements are true of false.

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

A:

Q: Prove that if the (n + 1) th derivative of a polynomial vanishes but the nth does not, then the…

A:

Q: Determine the degree of the Taylor polynomial Pn(x) expanded about a = 1 that should be used to…

A: f(x) =ln(x) =  Pn(x) + Rn(x)To approximate ln(2), centered at a=1, so that Rn(x) ≤0.001.…

Q: Find the Taylor polynomial of order 3 centered at 0. 1 f(x) = %3D 5-x x3 p3(x) = 25 125 625 x2 p3(x)…

A: Given: fx=15-x The Taylor series of above function when n=3. Taylor series is given by:…

Q: 2. Find the fourth Taylor polynomial for f (x) = In x at x = 1.

A:

Q: +∞ x sin(x2) : = - Σ n=0 (-1)" .4n+3 (2n + 1)! X

A: Let's find 7th degree maclaurin polynomial.

Q: Express p(x) = 1 + 2x -5x2 as a Taylor polynomial about a= -2.

A: p(x)=1+2x-5x2 a=-2

Q: Find two distinct cubic polynomials over Z2 that determine the same function from Z2 to Z2.

A: Given two distinct cubic polynomials over Z2 that determine the same function from Z2 to Z2.

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

A: We have given,

Q: Find the fifth Taylor polynomial of x3 - 7x2 + 8 at x = 0.

A: Given: fx=x3-7x2+8

Q: what is the lowest taylor polynomial that aproximates sin(0.1) with error at most 10^-6

A: Taylor series expansion of sinx is: sinx=x-x36+x520-x75040+.........

Q: 2. Find a Taylor polynomial of degree N=5 for f(x) = %3D 1+x xpanded about xo-0.

A:

Q: 8. Compute the Taylor polynomial of degree 4 about a = 1 for f(r) = 1/x. Write out the 1st 4 nonzero…

A: Given: f(x)=1x a=1

Q: The 2nd degree polynomial that interpolates to f(x) = cosx + sinx at x = 0, x= π/2 and x = π is best…

A: