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- 2. Find the interpolating polynomial using NDD of the points (0,0) , (1,16) , (2,48), (4,88) and (5,0)29. The area of the shaded region shown below can be represented as (2x + 6) (2x + 6) - (r(x + 3)²). . Is this representation a polynomial? Why or why not? Bi 2x + 6 x + 3 U Font Family AA A FEUse Algorithm 3.2 (Divided Difference) to construct the interpolating polynomial of degree three for the following data: f(1) = 1.2,f(2)= 1.6,f(4)=2, and f(5)=2.6 , then f(2.6)
- 10 In each part, use the Lagrange interpolation formula to construct the polynomial of smallest degree whose graph contains the following points. (a) (-2, –6), (-1,5), (1, 3) (Ъ) (-4, 24), (1, 9), (3, 3) (c) (-2,3), (–1, –6), (1,0), (3, –2) (d) (-3,–30), (-2, 7), (0, 15), (1, 10)Which of the following is the Lagrangian interpolation polynomial for the following points?Exercise 8.17 1. Find the products: (a)) (x - 3)² b) d) (x-5)(x-5) e) 9) (2x-1)(3x + 1) h) k i) (5 - 2x)(2x + 5) m) (2x + 3y)(3x - 2y) p) (2x+7)(3x - 6) (ax + by)² n q t Term 1 Week 8
- 2. Find (w + 1)(w-w+1).Letflx): 3x-2:9(x)-5x+1 Compute the indicated Values, a,lfogl(3) bfof) (oJ d, (go9) (-7) e. (fogof) (2) Sweet SelfieGiven (xi, x2024) Vi = 0,...,n, where x0 = -1, x₁ = 0, x2 = 1, x3 = 2, ..., xn = n = 1. Write down the interpolating polynomial with the least degree when (a) n = 1 (b) n = 2 (c) n = 2024 (d) n = 5000