To solve the equation 2sinx = x by Newton-Raphson method, the initial guess was chosen tobe x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration willbe closest toa)– 8.101b)1.901c)2.099d)12.101Correct answer is option 'B'. Can you explain this answer?

Question

To solve the equation 2sinx = x by Newton-Raphson method, the initial guess was chosen tobe x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration willbe closest toa)&ndash; 8.101b)1.901c)2.099d)12.101Correct answer is option 'B'. Can you explain this answer?

Answer

1.5708
b) 2.1699
c) 2.1834
d) 2.1863

Solution:
Given equation is 2sinx = x
Let f(x) = 2sinx - x
Using Newton-Raphson method, we have

x1 = x0 - f(x0)/f'(x0)

f(x) = 2sinx - x
f'(x) = 2cosx - 1

x0 = 2.0

f(x0) = 2sin(2.0) - 2.0 = -0.95892
f'(x0) = 2cos(2.0) - 1 = -0.83229

x1 = 2.0 - (-0.95892)/(-0.83229) = 2.1699

Therefore, the answer is (b) 2.1699.

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