GATE 2022 IN – Question 34
Newton–Raphson is applied to $f(x)=x-\cos x=0$. Starting with $x_0=0$, the next approximation $x_1$ is ______ (two decimal places).
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Correct answer: 0.99 to 1.01
Explanation
f(0)=−1 and f′(0)=1+sin0=1. Newton’s method updates x1=x0−f(x0)/f′(x0), using the tangent at the initial guess. Here x1=0−(−1)/1=**1.00**. This is one iteration, not a claim that 1 is the exact root.