GATE 2021 MT – Question 47
Use Newton–Raphson on $f(x)=x-\cos x$ with initial guess 0.5 radians. The root estimate after one iteration is ______ (three decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.745 to 0.770
Explanation
For f=x−cosx, f′=1+sinx.
Thus x1=0.5−(0.5−cos0.5)/(1+sin0.5)=0.755222. To three decimals, **0.755**.