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{"ops":[{"insert":"(For Questions 6 to 7 )"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Consider the nonlinear equation sin x \u2212 e"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"\u2212x = 0, which has a roots in the intervals [0, 1], [3, 4] and"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"[6, 7]."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Question 6 "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Which of the following is FALSE."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(1) The fixed-point formula g(x) = x + sin x \u2212 e"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"\u2212x converges to the approximate solution p ="},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"3.09636393 if the initial approximation is p0 = 1."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(2) Newton\u2019s method with p0 = 0.5 will converge to the approximate solution p = 0.588532744"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"after at most three iterations."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(3) The regula falsi method converges to p = 0.5885328664 if p0 = 0, p1 = 1 after ten iterations."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(4) Newton\u2019s method with p0 = 1 will converge to the approximate solution p = 0.588532743982"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"after exactly 4 iterations"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(5) The fixed-point method does not converge if p0 = 0.5."},{"insert":"\n"}]}

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