The sequence of values given by the iterative formula $$$x_{n+1}=\frac{6+8 x_{n}}{8+x_{n}^{2}}$$$ with initial value $$$x_{1}=2$$$ converges to $$$\alpha$$$. Use the iterative formula to find the value of $$$\alpha$$$ correct to 4 significant figures. Give the result of each iteration to 6 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_23 Year：2020 Question No：5(a)

Answer:

Use iteration correctly at least once
Obtain final answer $1.817$
Show sufficient iterations to 6 significant figures to justify answer or show sign change in interval $[1.8165,1.8175]$

Knowledge points:

2.6.3 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.)

Answer:

Knowledge points:

Solution:

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