Numerical Analysis: Perform the steps of the secant method to approximate the first three positive roots...

Numerical Analysis: Perform the steps of the secant method to approximate the first three positive roots of the transcendent equation x = sin (πx).

Expert Solution

Iteration scheme under secant method is:

Starting with for which (so we definitely have a positive root here) we get the following table of iterates:

n	x_n	f(x_n)
-1	2.000000000	2.000000000
0	0.500000000	-0.500000000
1	0.800000000	0.212214748
2	0.710610635	-0.078367145
3	0.734718088	-0.005508773
4	0.736540836	0.000176232
5	0.736484332	-0.000000363

Note that this equation has exactly one positive real root as can be seen from the graph below:

So the only positive root is (approximately)

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!

Colby Messinger answered 1 year ago

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