The GATE Grind

GATE 2016 ME (ME1) – Question 15

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 1 mark · Numerical answer

Solve $x=10\cos x$ by Newton–Raphson with initial guess $x=\pi/4$. The predicted root after the first iteration, to two decimal places, is ______.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 1.53 to 1.59

Explanation

Take f(x)=x−10cosx, so f-prime=1+10sinx. Starting atπ/4, Newton’s formula x1=x0−f(x0)/f-prime(x0) gives1.5641885. To two decimals this is **1.56**. Angles are in radians, as indicated by the initialπ/4.