Question

Find a real root of the equation cos(x) = 3x − 1 correct to four decimal places by using
method of successive approximation.

Answer 1

you want f(x) = cosx - 3x + 1 = 0
f(0) = 2
f(1) = cos(1) - 2 = -1.46
so f=0 somewhere on (0,1)
Now, using bisection,
f(1/2) = 0.377, so f=0 in (0.5,1)
f(0.75) = -0.51, so f=0 in (0.5,0.75)
repeat until you get 4 decimal places. x = 0.6071

If you have calculus, Newton's Method will converge much faster.

Answer 2

Find the real root of the four decimal x=3x-1

Answer 3

Find a real root of cosx − 3x + 5 = 0. Correct to four decimal places using the method of False Position method