Interpolate the function f(x) = ev3 on [-1, 1] with a second degree polynomial by using the zeros of appropriate Chebyshev polynomial. Hint: To(x) = 1, T1(x) = x and Tn+1(x) = 2xT,(x) – Tn-1(x) for n>1

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: Let k(x) = 1 -x4, where j(x) = y + k(x) and y = x6 - x2. Describe the graph of j(x) based on the…

A: Given: k(x)=1-x4 where, j(x)=y+ k(x) y=x6-x2 Then j(x)=x6-x2+1-x4j(x)=x6-x4-x2+1 The zeroes of the…

Q: 1. Determine a possible equation for each polynomial function. a) f(x)= d) f (x) = c) f(x) = f) f…

A: To find the equation of the given graph of function f(x) :-

Q: H.w Exl Let f(x)= 4x+2X+243and go)=3x+3x+3xx +4, where 2. t. f(x),900€75LX] Compute POX) +g (x).and…

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Q: Find the linear polynomial p(x) = a1x + ao, that interpolates the two points with coordinates (3, 0)…

A: Given query is to find the equation of the line.

Q: Find f(x) and g(x) such that h(x) = (fog)(x). 4 h(x) = (6x+3)* Choose the correct pair of functions.…

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Q: Find an equation in factored form for an even polynomial function with a local minimum at (2,0) and…

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Q: Let f(x) = 4+ (5x +9)³. Find f¹(x) = (1) · (√(x − 4) – 9) Find (ƒ(2)) -¹ = (¹) · (√(x-4) – 9)

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Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c>0. No sign change, by Descartes rule of…

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: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

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Q: Find functions f and g so that fo g=H. H(x)=√x² +12 Choose the correct pair of functions. O A. f(x)…

A: We have given a composite function  f○g=H Hx=x2+12 Checking pairs (f○g)x=fgx Afx=x , gx=x2+12…

Q: the function f(x) = k(x - s)(x - t)(x - u)^2 has: * O 3 zeros O 4 zeros O no turning points O 4…

A: Zeros of a function are those points where function has value zero. Hence f(x)=0 implies…

Q: 1 Let f(x) = x²-3x+2, g(x) = and h(x)=√1-x. Find f( - 6), g(-6), h(-6), h(a), and h(-x).

A: Let's evaluate the functions step by step. Given Functions 1.f(x)=x2−3x+2 2.g(x)=x​1​ 3.h(x)=1−x​…

Q: For the following polynomial:              f(x) = (x – 1)2 ( x^2– x – 30)   3a) Describe the end…

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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

Q: Q2 /| Find a cubic polynomial of x (5, 147). given points (0, 2), (1, 3), (2, 12),

A: Newton's divided differences interpolation

Q: Consider the function f(x)=x+2x.f(x)=x+2x. Construct the Lagrange interpolation polynomial which…

A: Lagrange's interpolation formula for n points can be defined as:…

Q: What is the domain of the radical function f(x)=√2x²-5x-12? D: (-∞0, ∞0) D: [-1.5, 4] D: [-1.5, ⁰⁰)…

A: The function is given byTo determine: The domain of the the function.Domain Restrictions for Square…

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: Suppose we want to form an interpolant at equally spaced points xo = 0, x1 = h, and x2 = 2h of the…

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Q: Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and…

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Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

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

Q: 1 using the divided-differences method. Consider the function f(x) =, rE-1,1]. Construct the…

A: Given function is fx=21+x2, x∈-1,1. We have to construct the interpolation polynomial which…

Q: Define f(x ) = Vx2 +1 and g(x) = 2 – x2. State the domain of (f + g)(x ). x # v2, –v2 - [-1, 00)…

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Q: Let b be a zero of f(x) = x5 + 2x + 4 Show that none of √2, ∛2, ∜2 belongs to Q(β).

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