7. Apply Newton's method to solve equation x³ – a = 0(a > 0), with initial guess xo > 0. If the Newton's sequence converges, what is its convergence order? Justify your answer. Solution: For the Newton's method, the convergence order is typi- cally 2. The Newton's iteration formula is 2 α 2x² + a Xk+1 = xk f(xk) f(k) 3k = -Xk+ 3x2²/ 3x²2/