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

Q: What are Bernstein polynomials?

A: A polynomial is basically a function, which can either be quadratic, cubic and so on in which the…

Q: 6 (iv) (v) (8) 5

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Q: QUESTION 2 Show how to find the cyclotomic polynomials Þ(x) for 1 ≤ n ≤ 15.

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Q: the greatest integer in x. Find f-1(B) when B=[0,2), Lot f:R→R F-R-R be dened by f(x) = [x]. the…

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Q: LOW: Construct polynomia -) sinx in [0, 2π] interpolation in mentioned interval of the function

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: Theorem 2.7. Let f be an arithmetical function which is not identically zero. If f is…

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Q: simplification is to isolate terms and identify the dominant term. For instance, we might want to…

A: fx(n) =log2log2n+3for n→∞log2n+3 =log2n

Q: Expand |x-d| in terms of Legendre polynomials.

A: To expand: 1x-d in terms of Legendre polynomials.

Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

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Q: (3) (a) Construct a polynomial p satisfying all the following properties simultaneously (give a…

A: construction of polynomial

Q: Question 12 Which of the following is a quartic polynomial function with zeros 1 (order 2), 2, and…

A: I have given the answer in the next step. Hope you understand that

Q: Let f, g = R[x] be polynomials, with deg g > 0. (a) The division rule for polynomials states that ƒ…

A: The objective is to solve the above question.

Q: 96.c)

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Q: t(n) = 7t(n-1) - 6 What is the smaller root (the root with smaller value) of the characteristic…

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

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Q: Question #2- find menimem degree sirlespdating polfnomial pero Compute fx). for Tne yollabing data…

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Q: Consider the Legendre polynomials of degree n Ph(x) = Σ (1)m 0<m</ where n is a nonnegative integer…

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Q: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

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Q: Write the recursive definitions suitable for the following functions in the fields in the table. f…

A: We have to write recursive definitions suitable for the following functions in the fields in the…

Q: Use the remainder theorem to evaluate the polynomial for the given values of x. h (x)=9x'-x-45x+5

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Q: Use the nspire calculator to integrate (b) Use the shorteut formulas to find L{81* – 5t² –…

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Q: 1. Legendre functions for n = 0. Show that (6) with n = 0 gives Po(x) = 1 and (7) gives (use In (1 +…

A: The given differential equation is (1-x2)y"-2xy'+n(n+1)y=0 and…

Q: What is the domaln of this exponentlal function?

A: Given query is to find the domain of exponential function.

Q: Show that 1.3.5... (2 n – 1) (i) P2n (0) = (– 1)" (ii) P2n+1 (0) = 0. 2.4.6 ... 2 n

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Q: Question 2 Prove that the polynomial f(x) = x2 + a2", n € N, a E R\ {0} is not divisible by g(x) =…

A: Factor theorem: The polynomial f(x) has a factor x-k if and only if f(k)=0. Given: f(x)=x2n+a2n,…

Q: of 9 - + Automatic Zoom 3 (5) For the functions f(x) = and g(x) =+ 4, find f(g(x)) and g(f(x)),…

A: According to the answering guidelines, we need to answer only the first question.  So, please repost…