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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 7"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Consider again the nonlinear equation sin x \u2212 e"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"\u2212x = 0. Applying the regula falsi method, with"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"starting point p0 = 3 and p1 = 4 and a tolerance of 10\u22125 yields the following result :"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(1) 0.589117 after at least three iterations"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(2) 0.588641 after at most three iteration"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(3) The method does not converge to a solution."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(4) 3.096308 after exactly three iterations"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(5) None of the above is true."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Consider now the function f(x) = x"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"4 \u2212 2x"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"3 \u2212 12x"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"2 + 16x \u2212 4 which has four distinct roots."},{"insert":"\n"}]}

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