Use the remainder theorem to find P (1) for P (x)=-2x'+4x² +3. Specifically, give the quotient and the remainder for the associated division and the value of P (1).

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: The fourth-degree polynomial f (x) = 230x* + 18x³ + 9x² – 221x - 9 has two real zeros, one in [-1,…

A: Bisection method: This method is also called the interval halving method and it is used to find the…

Q: Find a root of an equation f(x)=x²- x-1 using Bisection method

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Q: Find a polynomial of degree 4 with 9 as a zero of multiplicity 1 and 4 as a zero of multiplicity 3

A: A polynomial of degree n has a zero  a  of multiplicity k iff (x-a)k is a factor of polynomial

Q: Use the error term of a Taylor polynomial to estimate the degree of the Taylor polynomial which…

A: For a function being differentiable continuously for order n over an open interval, its Taylor…

Q: Find the polynomial that interpolates the function Vx at points x = 2,3,4 and 6 with cubic…

A: We will use Lagrange's interpolation method to first find the polynomial and then the approximation…

Q: The polynomial function f(x) = x² – 3x – 5 has two real zeros. |- (A) Determine (without iterating)…

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Q: Find the Taylor polynomial of degree 2 centered at a=-1 that approximate. f(x)=2+x+x2 P2(x)=

A: To find the Taylor Polynomial of degree 2 centered at a=-1 that approximate f(x)=2+x+x2.

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

A: it is known that taylor series about a point c is given by…

Q: Find the Taylor polynomial of order 3 generated by x at a. 1 f(x) -, a = 0 x+6

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

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

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Q: Let P(x) = 3–3x² +6x* be the fourth-degree Taylor polynomial for the function about x = 0. What is…

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Q: b) Used bisection method to find the root of f(x)= x³ + 3x-5, Do calculation until six iterations in…

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Q: Construct a polynomial with Rational Coefficients with: Even Degree · Roots of 1, 2, -3 y-intercept…

A: Given that:                    A polynomial with:   Even Degree   Roots of 1, 2, -3   y-intercept of…

Q: Use the remainder term to find a bound on the error in the approximation 1+1+ erval [-0.3, 0.3].

A: Given : f(x) = √(1 + x) ≈ 1 + π/2

Q: 7. Find a polynomial of degree 3 with zeroes -3, 2 and 3, passing through the point (0, 12).

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Q: Describe the accuracy of the nth-degree Taylor polynomial of f centered at c as the distance between…

A: We have to describe the accuracy of the nth- degree Taylor polynomial of f centered at c as the…

Q: Select the factors that multiply to create a polynomial with this description: (1) As x→-0, y→-∞ (2)…

A: Given x→-∞ and y→-∞ and x→∞ and y→∞ and x=4 is a root

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

A: Given:

Q: 2.1,2.-5, I 3. 9.)-2, 5 -3. 2 2 3 169-4,2 -3.4 .3,¢ 2

A: Note:- according to the company policy we can attempt ?️ only one question so please upload the next…

Q: 6. Find the first 4 terms of the Taylor polynomial of f (x) = 1/x centered at x = -2. Show your…

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

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Q: The estimate sqrt(1+x)=1+x/2 is used when x is small. Use the Remainder Estimation Theorem to…

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Q: . Find the Taylor polynomial p3 centered at a = 4 for ƒ(x) = 2/x. %3D

A: To find the Taylor polynomial p3 centered at a=4 for the given function f(x)

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: The average pollen count in a certain city on day x of the pollen season is P(x)=8x − 0.2x2 (for 0…

A: Consider the given function,  Represent the pollen count in a city on the day.   The day, which the…

Q: A car is moving with speed 20 m/s and acceleration 2 m/s? at a given instant. (a) Using a…

A: We  have to estimate the distance the car moves in the next second

Q: 2. Determine the polynomial equation with integral coefficients whose roots are -1, -2, and -3.

A: Answer and explanation is given below

Q: Find a polynomial of degree 3 with real coefficients and zeros of -3,-1,4 for which f(-2) =18

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Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

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Q: The fourth-degree polynomial f (x) = 230x4 + 18x³ + 9x² – 221x 9. - - has two real zeros, one in…

A: The given polynomial is - f(x)=230x4+18x3+9x2-221x-9 It is also given that the given function has…

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

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Q: Use bisection method to find the root of x^3 –x^2 – 3x – 3 with two initial points xl=3 and xr=2 and…

A: The given equation is x3-x2-3x-3=0. To find: the root between 2 and 3 .

Q: Express p(x)= x3 as a Taylor polynomial about a = -1.

A: The Taylor polynomial of degree n about  is given by:f(x) = f(a) + f'(a)(x-a) + f''(a)2!(x-a)2…

Q: Determine the values of x for which the function can be replaced by the Taylor polynomial if the…

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Q: 1.) Determine the absolute and relative error when approximating 2x8 using sixth-degree Taylor…

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Q: Find the Taylor polynomial of degree 4 about a = 1 for f(x) = 3/x. Write out the 1st 4 nonzero…

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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: The polynomial f (x) leaves the remainder x + 2 at the division with x ^ 2 + 2x-3 and leaves the…

A: Use the remainder theorem for the polynomials to determine the remainder when f(x) is divided by…

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 a polynomial of degree 5 with integer coefficients and has zeros ½, -i, and 1 – i, and leading…

A: Given,           The leading coefficient of the polynomial is 4 and zeros of the polynomial are 1/2,…

Q: what is the second degree taylor polynomial at a=4 for f(x)= sqrt. x on 3.8<x<4.2

A: Given:          fx=x          a=4 for second degree n=2 A taylor series is given by…

Q: The polynomial 1 + x + x²/2 is used to approximate f(x) = e*. Use the Remainder Estimation Theorem…

A: The polynomial 1+x+x22 is used to approximate f(x)=ex. Since we know that Taylor expansion for the…

Q: State the remainder formula for the nth Taylor polynomial of f(x) at x = a.

A: State the remainder formula for the nth Taylor polynomial of f(x) at x = a.

Polynomials

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