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جستجوهای پرتکرار

میتونی لایو بذاری!

a) By sketching a suitable pair of graphs, show that the equation

$\frac{1}{x} = \sin x$,

where $x$ is in radians, has only one root for $0 \lt x \leqslant \frac{1}{2}\pi $.

b) Verify by calculation that this root lies between $x = 1.1$ and $x = 1.2$.

c) Use the iterative formula ${x_{n + 1}} = \frac{1}{{\sin {x_n}}}$ to determine this root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.

پاسخ تشریحی :
نمایش پاسخ

a) Make a recognisable sketch of a relevant graph, e.g. $y = \sin x$ or $y = \frac{1}{x}$

Sketch a second relevant graph and justify the given statement

b) Consider sign of $\frac{1}{x} - \sin x$ at $x = 1.1$ and $x = 1.2$, or equivalent

Complete the argument correctly with appropriate calculations

c) Use the iterative formula correctly at least once

Obtain final answer 1.11

Show sufficient iterations to justify its accuracy to 2 d.p. or show there is a sign change in the interval (1.105, 1.115)

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