$$\( \)$$ Let $$\(\mathrm{f}(x)=\frac{\mathrm{e}^{2 x}+1}{\mathrm{e}^{2 x}-1}\)$$, for $$\(x>0\)$$ Use an iterative formula based on the equation in part (a) to determine a correct to 2 decimal places. Give the result of each iteration to 4 decimal places. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m21_qp_32 Year：2021 Question No：9(b)
Answer:
Use the iterative formula \(x_{n+1}=\frac{\mathrm{e}^{2 x_{n}}+1}{\mathrm{e}^{2 x_{n}}-1}\), or equivalent, correctly at least once
Obtain final answer \(1.20\)
Show sufficient iterations to \(4 \mathrm{dp}\) to justify \(1.20\) to \(2 \mathrm{dp}\), or show there is a sign change in the interval \((1.195,1.205)\)
Obtain final answer \(1.20\)
Show sufficient iterations to \(4 \mathrm{dp}\) to justify \(1.20\) to \(2 \mathrm{dp}\), or show there is a sign change in the interval \((1.195,1.205)\)
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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