Determine whether there is a choice of coefficients {a, b, c, d} for which the following function is a cubic spline. S(x) = S0(x) = 2(x + 1)^3 − (x + 1)^2 , −1 ≤ x ≤ 0           S1(x) = ax^3 + bx^2 + cx + d     , 0 ≤ x ≤ 1           S2(x) = (x − 1)^3 + 6                   , 1 ≤ x ≤ 2

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A: The surface is the part of z=x2+y2:

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Q: The Range of the quadratic function f(x) = -x² + 9x + 53 is O (0,4] O (-∞,53] O [53, ) O [-53, 4] O…

A: This question is based on finding range of quadratic function which is a downward opening parabola

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Q: 2. Determine whether each function is a polynomial function or another type of function. Justify…

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A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: 8. Describe the domain for h(x) = √70-9x - x²

A: To describe the domain for .

Q: Let (-1,(-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions?…

A: Given, -1,f(-1)=2,(0,f(0)=5) and 1,f(1)=6

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A: Newton's divided differences interpolation

Q: A graph of y=f(x) is shown, where f(x)=2x^5-3x^4+x^3-8x^2+5x+3 and f(-x)= -2x^5-3x^4-x^3-8x^2-5x+3.…

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Q: Let S be the part of the graph of the function x² + y² that lies above the disk x² + y² ≤ 4. What is…

A: The surface is the part of z=x2+y2:

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A: *to find:- roots of the given equation.

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A: The solution is given below.

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Q: 4. Are the following functions cubic splines? a. f(x) - x- 2x + 3, 0 sxs 1, - 2x - 3x2 + x + 2, 1 s…

A: Given :(a) f(x)=x3-2x+3, 0≤x≤1             =2x3-3x2+x+2, 1≤x≤2(b) f(x)=5x3-3x2+1 0≤x≤1…

Q: Given f(x) is defined on the closed interval [4, 20] where f(x) = −x^3 + 6x^2 + 288x + 4000 Find the…

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