Atividade Discursiva Cálculo Numérico

Resolução\n\nLk(x) = (x - x0)(x - x1) ... (x - xk-1)(x - xk) ... (x - xn)\n\nL0(x) = (x - x1)(x - x2)\n = (x - 7)(x - 10)\n = (x - 3)(x - 7)(3 - 10)\n\nL0(x) = (x^2 - 17x + 70) / 28\n\nf(x) L0(x) = 5 (x^2 - 17x + 70) / 28\n\nf(x) L0(x) = 0.18x^2 - 3.04x + 12.5\n\nL1(x) = (x - x0)(x - x1)\n = (x - 3)(x - 10)\n\nL2(x) = (x - x0)(x - x1)\n = (x - x3)(x - x7)\n\nL2(x) = (x^2 - 10x + 21) / 21\n\nf(x) L2(x) = 11 (x^2 - 10x + 21) / 21\n\nf(x) L2(x) = 0.52x^2 - 5.24x + 14\n\nP(x) = f(x0)L0(x) + f(x1)L1(x) + ... + f(xn)Ln(x)\n\nP(x) = f(x0) L0(x) + f(x1) L1(x) + f(x2) L2(x)\n\nP(x) = 0.18x^2 - 3.04x + 12.5 - 0.75x^2 + 9.75 - 22.5 + 5.24x + 11\n\nP(x) = -0.05x^2 + 1.47x + 1 / f(8) = p(8) = -0.05 + 6.47 - 8.1 + 9.56