Project ForgeEngineering Mathematics
Numerical Methods
GATE 2019
Medium
Newton-Raphson is used to find the root of f(x)=e^(−x)−x. With initial guess 0, the estimate after two iterations is (rounded off to three decimal places)
0.566(± 0.002 accepted)
Explanation
f'(x)=−e^(−x)−1. x1=0−f(0)/f'(0)=0−1/(−2)=0.5. x2=0.5−f(0.5)/f'(0.5)=0.5−0.10653/(−1.60653)=0.5+0.0663=0.566.
Source: GATE CH 2019 (2019)
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