Task 1 Sketch the curve y = 0.1x³-4 cos x a) Use your sketch to estimate the solutions of i) H) iii) 0.1x³-4 cos x = 0 0.1x³-4 cos x=4 0.1x³-4 cos x = x + 1 b) Find an estimate for the positive root by using two different iterative methods. Your answers should be accurate to 2 decimal places. Task 2 a) On the same axis plot (between the x values of -5 and 5) y = lnx and y = sin x Using your graphs find the value. of x for which In x = sin x b) By setting up an appropriate function, use two different iterative methods to validate your graphical estimate from part (a). Ensure your answers are correct to 2 decimal places.
Task 1 Sketch the curve y = 0.1x³-4 cos x a) Use your sketch to estimate the solutions of i) H) iii) 0.1x³-4 cos x = 0 0.1x³-4 cos x=4 0.1x³-4 cos x = x + 1 b) Find an estimate for the positive root by using two different iterative methods. Your answers should be accurate to 2 decimal places. Task 2 a) On the same axis plot (between the x values of -5 and 5) y = lnx and y = sin x Using your graphs find the value. of x for which In x = sin x b) By setting up an appropriate function, use two different iterative methods to validate your graphical estimate from part (a). Ensure your answers are correct to 2 decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Assignment brief and Guidance:
Task 1
Sketch the curve y = 0.1x³-4 cos x
a) Use your sketch to estimate the solutions of
0.1x³-4 cos x = 0
0.1x³-4 cos x = 4
0.1x² - 4 cos x = x + 1
i)
ii)
iii)
b) Find an estimate for the positive root by using two different iterative methods. Your answers
should be accurate to 2 decimal places.
Task 2
a) On the same axis plot (between the x values of -5 and 5)
y = lnx and y = sin x
Using your graphs find the value. of x for which In x = sin x
b) By setting up an appropriate function, use two different iterative methods to validate your
graphical estimate from part (a). Ensure your answers are correct to 2 decimal places.
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