Use the iterative formula $$\(x_{n+1}=2 \tan ^{-1}\left(\frac{1}{1+\mathrm{e}^{-x_{n}}}\right)\)$$ to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_33 Year：2021 Question No：6(c)
Answer:
Use the iterative formula correctly at least once
Obtain final answer \(1.34\)
Show sufficient iterations to 4 d.p. to justify \(1.34\) to 2 d.p. or show there is a sign change in the interval \((1.335,1.345)\)
Obtain final answer \(1.34\)
Show sufficient iterations to 4 d.p. to justify \(1.34\) to 2 d.p. or show there is a sign change in the interval \((1.335,1.345)\)
Knowledge points:
3.6.3 understand how a given simple iterative formula of the form relates to the equation being solved, and use a given iteration, or an iteration based on a given rearrangement of an equation, to determine a root to a prescribed degree of accuracy. (Knowledge of the condition for convergence is not included, but an understanding that an iteration may fail to converge is expected.)
Solution:
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