The constant $$\(a\)$$ is such that $$\(\int_{1}^{a} \frac{\ln x}{\sqrt{x}} \mathrm{~d} x=6\)$$. 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_w21_qp_31 Year：2021 Question No：8(c)
Answer:
Use the iterative process \(a_{n+1}=\exp \left(\frac{1}{\sqrt{a_{n}}}+2\right)\) correctly at least once
Obtain answer \(10.12\)
Show sufficient iterations to \(4 \mathrm{dp}\) to justify \(10.12\) to \(2 \mathrm{dp}\), or show there is a sign change in the interval \((10.115,10.125)\)
Obtain answer \(10.12\)
Show sufficient iterations to \(4 \mathrm{dp}\) to justify \(10.12\) to \(2 \mathrm{dp}\), or show there is a sign change in the interval \((10.115,10.125)\)
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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