Answer to Question #332123 in Algorithms for Jaguar

Question

(For Questions 6 to 7 )

Consider the nonlinear equation sin x − e

−x = 0, which has a roots in the intervals [0, 1], [3, 4] and

[6, 7].

Question 6

Which of the following is FALSE.

(1) The fixed-point formula g(x) = x + sin x − e

−x converges to the approximate solution p =

3.09636393 if the initial approximation is p0 = 1.

(2) Newton’s method with p0 = 0.5 will converge to the approximate solution p = 0.588532744

after at most three iterations.

(3) The regula falsi method converges to p = 0.5885328664 if p0 = 0, p1 = 1 after ten iterations.

(4) Newton’s method with p0 = 1 will converge to the approximate solution p = 0.588532743982

after exactly 4 iterations

(5) The fixed-point method does not converge if p0 = 0.5.

Answer 1

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