Theorem on Orthogonal Polynomials The sequence of polynomials defined inductively as follows is orthogonal Pn(x) = (x − an) Pn-1(x) — bn Pn-2(x) (n ≥ 2) with po(x) = 1, p₁(x) = x − a₁, and - an = : (XPn-1, Pn-1)/(Pn-1, Pn−1) : (xPn-1, Pn-2)/(Pn-2, Pn-2)

Q: Consider the function ?(?) =1/x and the data points ( 0.1, 10), (0.2, 5), (0.3,3.33) Find Lagrange…

A: Introduction: The formula of Lagrange interpolation polynomial is given by,…

Q: 2xy// + (x + 1)y/ +3y = 0

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Q: Let f(x) = x + √2x3 + x. Verify whether f[0, 1, 2, 3, 4] = f [0, 1, л, е, -1].

A: The details solution of the given question is given below in step 2.

Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: he absolute extrema of J(*) = ,2+2x +9 n(-1,5]. %3D

A: The given function is  f(x)=xx2+2x+9 on [-1,5]

Q: Verify that the factorization for f (x) = x3 + x2 + 1 over Z2

A: Given that, fx=x3+x2+1. Also ℤ2=0, 1 To verify the factorization for fx over ℤ2.

Q: f(x) = 8+x 8 - x on [4, 6].

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Q: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88    0.75…

A: Given: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88…

Q: 1- Suppose A=

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Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

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Q: Find Absolute Max and Min: f(x) = x2 – 2x On [0, 1] Ab. Max = when x= Ab. Min = when x=

A: For the given  f(x) = x2-2x3 at [0,1] Absolute maxima and absolute minima is calculated as shown…

Q: '(x) = ( 13 + x1, (x-1)², x x

A: T(x)=|3+x|x<-1(x-1)2x≥-1

Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

Q: Let f(x) = x* - 3x2 + 2 be a polynomial function. Which one the following intervals, the function…

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Q: Find the range of the function f(x) = x2-1 O [-2,21 R\[-1] R\{0}

A: Range of function

Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

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Q: What is the point of intersection for f(x) = 2* and g(x) = A (1,0) (1, )

A: Here we have to find the point of intersection of f(x)=2x ............................... (1)  and…

Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

A: The given function is fx=11-x. Replace x by x+h and obtain that, fx+h=11-x+h. Obtain the difference…

Q: Consider the function f(x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f(x)…

A: First derivative check for monotonicity

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

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Q: B. Let f(x) = x – x - 4 and g(x) = 2x – 6 4.) Find ()(x - 1) 5.) Find (4) (x)

A: topic - functions

Q: fex)= J4-x +2

A: The function is given by f(x) = 4-x + 2 To evaluate : The graph of the function f(x)