(a) Find the Maclaurin polynomial p2 for V1- x and express the error with Landau's big O notation. (b) Use the result of part (a) to show that 2/1 – x +x - 2 = L + O(x) x2 as x → 0, where the constant L is to be determined. That is, find L.

Q: Now let f(x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For…

A: We will use repeated differentiation to prove this

Q: 3. Let p(x) = 6xª – 13x³ + 13x² – 2. - (a) Find q(x) such that p(x) = (2x – 1)q(x) using synthetic…

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Q: USE the synthetic method of division to divide the polynomial f(x) = r" – 32 by d(r) -2.

A:

Q: (10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of…

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Q: find the real polynomial f(x) which has zeros x=1 (multiplicity 2) and x=2+i (multiplicity 1). you…

A: We have given the zeros x = 1 with multiplicity 2 and x = 2+i with multiplicity 1.

Q: Find the polynomial of degree four or less that fits the unequally- spaced arguments of x: -0.2,…

A: We have to find the polynomial of degree four or less that fits the given unequally-spaced…

Q: Which of the following polynomial functions has a graph that crosses the x- axis at (-4,0)? A. f(x)…

A: Let's find.

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Newton's Divided Difference table is given by x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl…

Q: For the polynomial f (x) = x³ – 2a² – 5æ + 6 what is the end behavior as x x → ±∞ - O x → 0 → +∞ 8.…

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Q: For the polynomial Ax) = 13(x – 6)(66 – 37x²) (a) Report the exact values of the zeros. 66 66 -6 37'…

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

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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: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Let s(t) be the distance of a truck to an intersection. At time t = 0, the truck is 60 m from the…

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Q: For the polynomial below, 1 is a zero. h(x) =x- 7x + 10x- 4 x=(x)4 Express h (x) as a product of…

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Q: Give the degree and leading coefficient of the following polynomial function. f (x) = x³ (3 – 7x² –…

A: Here in the given polynomial, we have to find the degree and order of the polynomial.   The highest…