i. By sketching a suitable pair of graphs, show that the equation e 2x = 14

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i. By sketching a suitable pair of graphs, show that the equation e^2x = 14 − x² has exactly two real roots.

ii. Show by calculation that the positive root lies between 1.2 and 1.3.

iii. Show that this root also satisfies the equation x = 1/2 In(14 - x²).

iv. Use an iteration process based on the equation in part iii, with a suitable starting value, to find the root correct to 2 decimal places. Give the result of each step of the process to 4 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 28, 2023 02:59 AM

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i. By sketching a suitable pair of graphs, show that the equation e 2x = 14

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Step by Step Answer:

i To sketch a suitable pair of graphs lets first rewrite the equation as x2 2x 14 e2x 0 Now let fx x2 2x 14 and gx e2x Then our equation can be writte...View the full answer

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

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