Para encontrar a raiz quadrada de 7 utilizando o método de Newton, partimos de um chute inicial \( x_0 = 2 \) e aplicamos o método iterativamente até que os valores de \( x_i \) se estabilizem, ou seja, até que não haja mudança significativa nos valores a cada iteração. O método de Newton para encontrar raízes quadradas é dado por: \[ x_{i+1} = \frac{1}{2} \left( x_i + \frac{7}{x_i} \right) \] Vamos realizar as iterações: 1. \( x_1 = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + \frac{7}{2} \right) = \frac{1}{2} \left( 2 + 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