Allied & ICAR Exam Bank • ALLIED_2762 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

Applying Newton–Raphson to find the reciprocal of $N = 4$ via $f(x) = \frac{1}{x} - 4 = 0$ with $x_0 = 0.2$, the next iterate $x_1 = x_0(2 - N x_0)$ is:

Answer Key:

0.24

Step-by-Step Solution & Explanation

$x_1 = 0.2(2 - 4 \times 0.2) = 0.2(2 - 0.8) = 0.2(1.2) = 0.24$.
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