The diagram shows the curve $$$y=\frac{\tan ^{-1} x}{\sqrt{x}}$$$ and its maximum point $$$M$$$ where $$$x=a$$$. 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. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_31 Year：2021 Question No：7(c)

Answer:

Use the iterative process $a_{n+1}=\tan \left(\frac{2 a_{n}}{1+a_{n}^{2}}\right)$ correctly at least twice
Obtain final answer $1.39$
Show sufficient iterations to at least 4 d.p. to justify $1.39$ to 2 d.p. or show there is a sign change in the interval $(1.385,1.395)$

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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