Question 2: Create a polynomial f(x) with real number coefficients which has the following characteristics: • f is degree 5. • x = 6, x = i and x = 1 - 3i are the zeros of f. • As x → - co, f(x)→ co

Q: 1. Find the first, second, third and fourth order Maclaurin polynomials of f(x) = arctan(x). Draw…

A: f(x)=tan-1x To find the first, second, third and the fourth order Maclaurin polynomial of f(x) To…

Q: f(x) = ao + a,x + azx² + azx³ € R[x] polinomu için –2 e R, f(x) polinomunun bir kökü ise x+2 e R[x]…

A: As ℝ is a ring of real numbers. So ℝ[x] is the polynomial ring that contains all polynomials in x…

Q: Given a function f(x). Suppose that Newton's interpolating polynomial P₂ (x) of f(x) at the points…

A:

Q: What are the rational roots of the polynomial P(x) = æ³ + 3a? + æ – 1? * = -1 O a = 0, a = ±1 Oæ =…

A: P(x)=x3+3x2+x-1 To find the rational roots of the polynomial To select correct option

Q: 4. Find the polynomial function f(x) of degree 4 with zeros 2 (multiplicity 2) and 3i, f(0) =36

A:

Q: Ax) = eV cos(x) +:

A:

Q: Calculate the first three Legendre coefficients for f (x) = x2 - 1 and then express the f(x) in…

A: Recall the definition of Legendre polynomials.

Q: Let p be a polynomial of degree n and let  S = { x is an element in interval (0,pi/2) | cos(x) =…

A:

Q: 4. Let F(x) be a polynomial function such that F(4) =-1 and F'(4) = 0. If x 4, then F'(x) > 0, what…

A: Given that  F(x) be a polynomial function such that F(4) = -1 and F'(4) = 0. Also F'(x) < 0 when…

Q: 10.2. Let f(x) = 3x³ + x* + x³ + 3x? + 2x +4 and g(x) = 2x³ + 3x² + x +1 be polynomials in Zs[x].…

A: Given that f(x)=3x5+x4+x3+3x2+2x+4 , g(x)=2x3+3x2+x+1 To find q(x) ,r(x): Here Dividend is…

Q: 3. Let P(x) be a polynomial of degree n. If n is even, prove P(x) cannot have an inverse function.

A:

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

A:

Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

A:

Q: 4. Consider the polynomial f(x) = x² + 1. (a) Show that f(x) is irreducible in (Z/3Z) [x]. (b) Show…

A:

Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

A: Given function is  Fx=∫1xsin2tdt

Q: The Maclaurin polynomial of degree 4 for the function f(x) = cos(x) is %3D

A:

Q: 2. Consider the Newton polynomial Pn(x) = ao+a1(xr-xo) + a₂(x-xo)(x − x₁) +... +an(x-xo)(x -…

A: Given that   that interpolate then we have Now  ,       putting

Q: 1. Find the 4th order Maclaurin polynomial for f(x) and apply it to approximating f (0.12) a. f(x) =…

A: The given functions, a) fx=e2x b) fx=sin2x We have to find the fourth order Maclaurin polynomial and…

Q: ƒ(X) e F[X] be a non-constant polynomial of degree d. Prove that f(a) has degree at least over F.

A: ANSWER :

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ E R. -

A: Given, x.f(x-1)=x-3.f(x),  ∀x∈R put x=0 in equation 0×f(-1)=-3f(0)f(0)=0 put x=1…

Q: Construct the Langvange inter po lation polynomial for the function y= Sin Tx, taking the points %3D…

A:

Q: a) The roots of a degree 4 polynomial f(x) are 0, –1, 1, 1. Suppose f(2) = -1. Find a formula for…

A: Given query is to find the polynomial and interval where it is positive and negative.

Q: 3. Let P be the set of polynomials with real coefficients and with degree > 1. If f € P, let Af = {x…

A:

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

A:

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

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