A curve has equation $$$y=x^{3} \mathrm{e}^{0.2 x}$$$ where $$$x \geqslant 0$$$. At the point $$$P$$$ on the curve, the gradient of the curve is 15 . Use an iterative formula, based on the equation in part (a), to find the $$$x$$$-coordinate of $$$P$$$ correct to 4 significant figures. Give the result of each iteration to 6 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m20_qp_22 Year：2020 Question No：6(c)

Answer:

Use iterative process correctly at least once
Obtain final answer $1.771$
Show sufficient iterations to 6 sf to justify answer or show a sign change in the interval
$[1.7705,1.7715]$

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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