The equation of a curve is $$$y=\sqrt{\tan x}$$$, for $$$0 \leqslant x<\frac{1}{2} \pi$$$. Use the iterative formula $$$ a_{n+1}=\tan ^{-1}\left(\frac{1}{3}\left(1-\tan ^{2} a_{n}-\tan ^{3} a_{n}\right)\right) $$$ to determine $$$a$$$ correct to 2 decimal places, giving the result of each iteration to 4 decimal places. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_32 Year：2021 Question No：11(c)

Answer:

Use the iterative process correctly with the given formula at least once
Obtain final answer $a=0.29$
Show sufficient iterations to 4 d.p. to justify $0.29$ to 2 d.p., or show there is a sign change in $(0.285,0.295)$

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.)

Answer:

Knowledge points:

Solution:

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