{1 + x + x, x + x², for P2. Let >(x) = p(x)]B = 1 + 3x + 2x2. The

Q: ivative of p = 2xz nes maximum in t 3k

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Q: Use the def'n of to test the dif ferentiability of the x=0 : ヘ人る given gn at Sx²+2x-1, x<o ○け f(x) =…

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Q: Find k such that f(x) = x3 - kx2 + kx + 2 has the factor x - 2.

A: The general polynomial equation of degree n  is an equation of the form…

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree polynomial for f(x) = using Lagrange Interpolation is

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Q: Given the function C(x) = (– 8x + 2)"( – 12x – 7)°, - - its zeros are and their multipicities are

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Q: For which n E N is the polynomial f(x) = x^(2n) + x^n + 1 divisible by g(x) = x^2 + x + 1?​

A: To find the value of n ∈ ℕ for which the polynomial f(x) = x2n + xn + 1 is divisible by g(x) = x2 +…

Q: (b) Suppose that f(x) : УBx2 — 3 (Bx +2 if if x 2 Find the value of ß so that f(x) is continuous…

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Q: Given that f(x)=x^2-19x+90f(x)=x2−19x+90 and g(x)=x-10g(x)=x−10, find (f\div g)(x)(f÷g)(x) and…

A: The given functions are f(x)=x2-19x+90 and g(x)=x-10.

Q: Let ƒ(x) = x3 - x - 1. Use the Intermediate Value Theorem to show that ƒ has a zero between -1 and…

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Q: Find Valume x zO; Ekort the X3D2; 0 about the x- axis

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Q: Given the function f(x) = 2x3 – 11.7x? + 17.7x – 5, find one root using Secant Method with an…

A: Consider the given equation, fx=2x3-11.7x2+17.7x-5 Now, define the secant method.…

Q: 29. For |x|<1, prove that 24x 1-x 16x 8x 1 + 1-x1+x ....... 8x &r = 1+ (1- x) (1 +x)2 ' (1-x)2 ...

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Q: Find k such that f(x) = x4 - kx3 + kx2 + 1 has the factor x + 2.

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Q: Find the maximum of f (x) = 4x – 1.8x? + 1.2x³ – 0.3x* using Quadratic interpolation (xo = 1.75, x1…

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Q: Let f(x) = x³ + x + 4 and g(x) = 3x + 2 in Zs[x]. Then, upon dividing %3D f(x) by g(x), we get None…

A: f(x)=x3+x+4 and g(x)=3x+2 in Z5[x].

Q: 4. Consider f(x) = 2x² + 3 on the closed interval I = [0, 4].

A: I have Provided this answer in step-2. i have given an only one answer because as per our policy.

Q: 3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the %3D %3D Intermediate…

A: By rule we solve only first question i.e. Q3 3) Given f(x)=x4-4x2+6g(x)=3x3-8xTo prove the functions…

Q: Does f(x) = x - x - 5 have a real zero between 1 and 2? %3D

A: f(x)=x3-x-5 have a zero between 1 and 2.

Q: Let f(x) = x³ +x + 4 and g(x) = 3x + 2 in Zs[x). Then, upon dividing f(x) by g(x), we get None of…

A: Every integer polynomial we can write as an polynomial in Z5(x). Using this idea again and again we…

Q: @ f(x)= x²-3x-4 2 @ f(x) = x² - 4x +3 Show that whether f(x) reduceable Poly or not

A: The given problem is solved below in detail.

Q: 14) Use the Intermediate Value Theorem to show that the po zero in the given interval. g(x) = 2x³ –…

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Q: 1) Find the absolute extremum values of f(x)=x2-4x+20f(x)%3DX2-4x+20 over the interval [1,4][1,4].

A: The extrema value of  function is f(4)=20

Q: Prove that you can find a polynomial p(x) = Ax2 + Bx + C that passes through any three points (x1,…

A: we have to prove that we can always find a polynomial p(x) = Ax2 + Bx + C that  passes through any…

Q: 27. Factor f(x) = 15x – 67x + 26x + 8, given that is a zero of f(x).

A:

Q: 6. (a) Express f (x), where x3 + 1 f(x) = %3D (x – 1)2 (x² + 1) Hence, or, otherwise, find HE AND…

A: f(x)=x3+1(x-1)2(x2+1)

Q: Find the integer a in Z5 so that (x-a) become a divider for f(x)=x^3+2x^2+3x+3 over Z5[x]

A: We have to find an a∈Z5 such that x-a is a divider for the polynomial fx=x3+2x2+3x+3 over Z5x. If…

Q: Show that f (x) = 3x² - x - 1 is O(x²) with suitable C and k.

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Q: Find all n EN for which is the polynomial x2n + x" +1 divisible by (x)f g(x) = x² + x + 1?

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Q: 3. For f (x) = 2x³ + 4x² + 3x – 7, prove that there exist a number k such that f(k) = 20.

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Q: Find the Domain (b) g(x) = In(x² –- x) %3D

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Q: Find the maximum of f (x) = 4x – 1.8x² + 1.2x3 – 0.3x* using Quadratic interpolation (xo = 1.75, x,…

A: We can solve this using quadratic interpolation formula

Q: (4) Let f(x) = xª + 2x³ + 6x² + x – 1. Find, with proof, the number of zeroes of f.

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Q: Let f(x) = 5x4 + 3x3 + 1 and g(x) =3x2 + 2x + 1 in Z7[x].  Determine the quotient and the remainder…

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Q: find n∈ℕ is the polynomial f(x)=x2n +xn+1 divisible by g(x)=x2 +x+1?​

A: Given:            f(x)=x2n+xn+1             gx=x2+x+1

Q: Find a function P(x) of least possible degree, having real coefficients, with the given zeros. 03…

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Q: Q2) If f(x) = (x), and g(x) = (2- x)i find (gof) (x) and the domain of (gof)(x).

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Q: on is discontinuous on the specified interval. Vx2 - 64 if IS -8 if-8<x<8 88] 0 ifx28 f(x) = {x+8

A: If a function is continuous then the left hand limit, right hand limit and value of function at that…

Q: a51 - Find ax2@y3 if f(x,y)-x.e z

A:

Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Q: h(x)=-5-5x.

A: Given polynomial is                               h(x) = -5 - 5x

Q: 2/3 of f(x) = (x²4)73. (b) Find all critical nurabers

A: There are multiple question. As per company policy kindly ask other question separately. b.

Q: 5. Find the absolute maxima or minima for f(x) = x² + 8x + 3 over the open interval (-o, 0).

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Q: on the closed interval Co,14], (0,14)such that f'ccF FC14D-FCO) 14-0

A: we have to find the value of c

Q: 3 By applying the Intermediate Value Theorem choose the interval over which x4 = 7x3 - 5 will have a…

A: The given problem is to find the interval for the given function that which the intermediate value…

Q: express the quotient  P(x)/D(x)  in the form  P(x) D(x) = Q(x) +  R(x) D(x). P(x) = 8x2 − 3x − 17,…

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Q: For f(x)=2x3+4x2+3x-7, prove that there exist a number k such that f(k)=20.

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Q: Givenf (x) = for x # 3; ƒ-l (x) = ? x - 3 Of-1 (x) = 3+2 x-1 Of-l (x) = 3x+2 x-1 X- f-' (x) = 2 x+1…

A: Steps Rewrite f(x) as y Swap x and y Solve of y.

Q: True or False The domain of 1f # g2 1x2 consists of thenumbers x that are in the domains of both f…

A: The domain of (f·g)(x) consists of the numbers x that are in the domains of both f and g

Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33

Q: Determine the roots of f (x) =-12-21x + 18r - 2.75x using the false-position method, with initial…

A:

Polynomials

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