Use-Newtown-Raphson-method-to-find-aproximate-value-of-X-7-x-1-starting-with-x-0-2-perform-4-iteration-and-all-iteration-should-be-presented-in-4-decimal-places-

Question Number 12612 by frank ntulah last updated on 26/Apr/17

Use Newtown Raphson method to find aproximate

value of X = \sqrt{(\frac{7}{x + 1})}, starting with x_{0} = 2 .

p e r f o r m 4 i t e r a t i o n a n d a l l i t e r a t i o n

s h o u l d b e p r e s e n t e d i n 4 d e c i m a l p l a c e s

Answered by mrW1 last updated on 26/Apr/17

f (x) = \sqrt{\frac{7}{x + 1}} - x

f^{'} (x) = \frac{1}{2 \sqrt{\frac{7}{x + 1}}} \times \frac{- 7}{{(x + 1)}^{2}} - 1

\frac{f (x)}{f^{'} (x)} = - \frac{\sqrt{\frac{7}{x + 1}} - x}{\frac{1}{2 \sqrt{\frac{7}{x + 1}}} \times \frac{7}{{(x + 1)}^{2}} + 1} = - \frac{\frac{7}{x + 1} - x \sqrt{\frac{7}{x + 1}}}{\frac{7}{2 {(x + 1)}^{2}} + \sqrt{\frac{7}{x + 1}}}

= - \frac{14 (x + 1) - 2 x \sqrt{7 {(x + 1)}^{3}}}{7 + 2 \sqrt{7 {(x + 1)}^{3}}} = g (x)

x_{n + 1} = x_{n} - \frac{f (x_{n})}{f^{'} (x_{n})} = x_{n} - g (x_{n})

x_{0} = 2

x_{1} = x_{0} - g (x_{0}) = 2 - g (2) = 1.6234

x_{2} = x_{1} - g (x_{1}) = 1.6234 - g (1.6234) = 1.6310

x_{3} = x_{2} - g (x_{2}) = 1.6310 - g (1.6310) = 1.6311

x_{4} = x_{2} - g (x_{3}) = 1.6311 - g (1.6311) = 1.6311

\Rightarrow x \approx 1.6311

Commented by frank ntulah last updated on 27/Apr/17

God bless you sir