State the following statement is True or False
According to the Newton-Raphson's method the approximate root of the equation $f (x) = 0$ is $x_{n}$ then be $x_{n} = x_{n + 1} - \frac{f (x)}{f^{'} (x_{n})}$ .

True

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False

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Solution

The correct option is B False
If $x_{n}$ is the approximate root of $f (x) = 0$ then the value of $x_{n}$ given by Iterative eqn. for Newton-Raphson method is
$x_{n + 1} = x_{n} - \frac{f (x_{n})}{f^{'} (x_{n})}$ , where $f^{'} (x_{n})$ is derivative of $f$ at $x_{n}$

$∴$ The given statement is FALSE.

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