Use Newton's method to approximate a root of the equation 5 x^7 + 5 x ^4+ 2 =0 as follows.
Let x_1 = 2 be the initial approximation.
The second approximation x_2 is
and the third approximation x_3 is
Can someone give me some help on this
this is just an iteration of a well known formula ... I suggest you research it.
Pauls Online Notes : Calculus I - Newton's Method
Each Newton's iteration is...
$\displaystyle \displaystyle x_{n+1} = x_{n} - \frac{f(x_{n})}{f^{'} (x_{n})}$ (1)
In Your case is...
$\displaystyle f(x) = 5\ x^{7} + 5\ x^{4} + 2$
$\displaystyle f^{'} (x) = 35\ x^{6} +20 \ x^{3}$ (2)
... so that setting $\displaystyle x_{1} = 2$ in (2) and then evaluating (1) You obtain $\displaystyle x_{2} = 1.6991166....$... then You set $\displaystyle x_{2}$ in (2) and then evaluate (1) and obtain $\displaystyle x_{3}$... then...
Kind regards
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