Project ForgeEngineering Mathematics
Numerical Methods
GATE 2012
Medium
The Newton-Raphson method is used to find the roots of the equation f(x)=x−cos(πx), 0≤x≤1. If the initial guess for the root is 0.5, then the value of x after the first iteration is
- A1.02
- B0.62
- C0.55
- 0.38
Explanation
f(x)=x−cos(πx), f'(x)=1+π sin(πx). At x0=0.5: f(0.5)=0.5−cos(π/2)=0.5−0=0.5; f'(0.5)=1+π sin(π/2)=1+π=4.1416. x1=x0−f(x0)/f'(x0)=0.5−0.5/4.1416≈0.5−0.1207=0.379≈0.38.
Source: GATE CH 2012 (2012)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.