To calculate 1/a using N-R method,
Set up the equations as x = 1/a
i.e 1/x = a
→ 1/x – a = 0
i.e f (x) = 1/x – a = 0
Now f(x) = - 1/(9x^2)
F(x_k) = 1/(x^2) – a
F() = -1/ \[(x_k)^2\]
For N-R method, \[x_{k+1} = x_k -f(x_k)/f'(x_k)\]
Simplifying which we get \[x_(k+1) = 2x_k - ax_k^2\]
For a = 7 and starting with \[x_{k+1} = 2x_k - ax_k^2 \]
For a = 7 the iteration equation,
Becomes\[ x_{k+1} = 2x_k – 7(x_k)^2\]
With x0 = 0.2
X1 = 2\[(x_0)\] - \[7x_0^2\] 2 × 0.2 - 7 (0.2 )2 = 0.12
and \[x_2\] = 2\[x_1\]– 7x12 = 2×0.12-7(0.12)2 = 0.1392
