Project ForgeEngineering Mathematics
Calculus
GATE 2016
Medium
Solve the equation x = 10cos(x) using the Newton-Raphson method. The initial guess is x = π/4. The value of the predicted root after the first iteration, up to second decimal, is __________.
1.56(± 0.03 accepted)
Explanation
f(x)=x-10cos(x), f'(x)=1+10sin(x). At x0=π/4≈0.7854: f(x0)=0.7854-10(0.7071)=-6.286, f'(x0)=1+10(0.7071)=8.071. x1=x0-f(x0)/f'(x0)=0.7854+0.779≈1.56.
Source: GATE ME 2016 Set-1 (2016)
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