The equation cosec x = x 2 has a root, , between 1 and 2. The equation

Question:

The equation cosec x = x² has a root, α, between 1 and 2.

The equation can be rearranged either as

a. Write down two possible iterative formulae, one based on each given rearrangement. Use the starting value 1.5.

b. Show that one of the formulae from part a fails to converge.

c. Show that the other formula from part a converges to α and find the value of part α correct to 3 decimal places. Give the result of each iteration to 5 decimal places.

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Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

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Question Posted: Mar 24, 2023 02:04 AM

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The equation cosec x = x 2 has a root, , between 1 and 2. The equation

Question:

x = sin-1 (+) or x = 1 V sin x

Step by Step Answer:

Answer a The two possible iterative formulae are Based on x sin1x x sin1x with x 15 Based on x 1sinx ...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

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