Topic: interpolation and polynomial approximation             1 + 2x - x3 , on [ 0 , 1] f(x) = {               2 + a(x-1) + b(x-1)2 + c(x-1)3 , on [1,2] from the functions piecewise function given above, find the values of a,b,c that will make the f(x) a natural cubic spline on [ 0,2]

Q: Find the zeros of the polynomial f (x) = x³ – x2 + 4x – 4 О 1,2, -2 O -1, 2, -2 О 1,21, -2i O -1,…

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Q: Sketch a cubic function (third degree polynomial function) y = p(x) where p(x) > 0 on the intervals…

A: The solution is shown below-

Q: 1 Find the domain of the function f(x,y) = 128 - 256(4x + 8y – 56) Domain D= {(x,y) : #0} Express…

A: we have to find domain of the given function f

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Using Rouché’s Theorem, show that the polynomial h(z) = 10z^4 + 12z^3 + 1 has three zeros with |z| <…

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Q: A) f(x) = -(x-3)(* +4) ...... 15 B) f(x) = 3(x + 4)(x-3) .... C) f(x) = -(x - 1)? + 2 ...... -15 -10…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Zero of 5+ i, 4-i, and f(0) = 1 DC=Sti/ x=4-1 (r-sti) (x²+4-i)

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Q: 6. Determine an equation and provide a sketch for a polynomial function with the following…

A: An equation of polynomial function with the following characteristicsQuartic function (polynomial…

Q: A small aircraft starts its descent from an altitude of h = miles, 4 miles west of the runway (see…

A: Here given function as fx=ax3+bx2+cx+d .....1 where x∈-4, 0 Also, from the given figure,  f-4=h=23…

Q: The cubic polynomial f(x) is defined by f(x)=6x^3-5x Find the reminder when is divided by(x+4) Show…

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Q: Example 2: Using the False Position method, find an approximated root of the function: f(x) = x² –…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: Runge's function is written as f (x) = 1 1+ 25x² Generate five equidistantly spaced values of this…

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Q: Determine a possible 3rd degree polynomial function in factored form with its only (3, 0) and (-2,…

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Q: Use the given information to graph the unknown polynomial 1.) Given: Y-intercept at (0,3)…

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Q: #1: WITHOUT graphing, identify the end behavior of the polynomial function. 4] y = 6 – 2x – 4x² +…

A: topic ,- polynomials

Q: 74. (-300, 0) 400 f(x) 210 1-10² (100, 0) 100 200 −1-10³) (0, –90,000) -2-10 -200 -100 3-10³.

A: For any polynomial equation from graphics can be given by as:  F(x)  = a(x-b)  (x-c)  (x-d)  Where…

Q: How to find the cubic polynomial function that has zeros of x=2, x=3(+or -) i

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Q: A quadratic function is defined by PC = (x-1) (x+3) Graph the function on the Coordinate plane Y 5 3…

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Q: -3 -2 -1 IV 8 6 4 NA 2 o -2 4 -6 2 The graph shows a polynomial function f(x) of degree 3. Which…

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Q: (a) Write polynomial function for Zeros;-1, 3, -2 with multiplicity 2, 1, 3 respectively 2.. רודא

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Q: (b) (2 points) use the Concavity Theorem to determine where f(x) is concave up and where it is…

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Q: Form a polynomial whose zeros and degree are given. 1) Zeros: -3, -2, 2; degree 3 A) f(x)=x3-3x2 -…

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Q: The zeros of the polynomial P(x) = x* - 5x2 + 4 are (a) 2i, -2i, i and - i (b) 2,-2, i and – i (c)…

A: We have to choose the correct answer

Q: 3) Given the cubic function f(x) 3 2 x² + 3x² 13x 15. a) Put f(x) in factored form, show your work…

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Q: Given f(x) = 2(x - 1)(x + 3)³(5x + 1)^(x − 3)¹ List the zeroes (ex. 4, 6, -2): Degree: End behavior:…

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Q: Find an 4th degree polynomial function with real coefficients whose zeros are 4,–1,2, v2i and a…

A: Here degree of polynomial is 4 so it has 4 roots.

Q: x-4 f(x)=2x+2 Determine the domain of a) ({x|x*1,xER}) Ob) ({x/x = − 1, x = R}) c) ({x|x*-1, XER})…

A: Given function is

Q: Use the graph to the left to sketch f'(x) with the given information: f'(x) is a polynomial with…

A: Given f'x is a polynomial of zeros 3,0 and -2 and multiplicity of x =-2 is 2f'x is maximum at x =-1…