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Use Newton’s method with the specified initial approximation x1 to find x3. 
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#1
Jul1410, 10:15 PM

P: 157

Please verify my answer.
1. The problem statement, all variables and given/known data Use Newton’s method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.) x^5+2=0, x_1=1 2. Relevant equations 3. The attempt at a solution x^{5}+2=0, x_{1}=1 y'=5x^{4} x_{(n+1)}=x_{n}(x^{5}+2)/(5x^{4} ) For n=1 x_{2}=1((1)^{5}+2)/(5(1)^{4} )=6/5=1.2 For n=2 x_{3}=1.2((1.2)^{5}+2)/(5(1.2)^{4} )= 1.20.4883/10.368=1.2+0.047=1.1530 


#2
Jul1510, 06:52 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,553

x_{(n+1)}=x_{n}(x_{n}^{5}+2)/(5x_{n}^{4} ) 


#3
Jul1510, 11:34 AM

P: 157

Hi! What do you mean by
The task says to do the third approximation, which I found already.... Do you mean I should do the fourth...and the fifth?... 


#4
Jul1510, 12:34 PM

Mentor
P: 21,294

Use Newton’s method with the specified initial approximation x1 to find x3.
I think that HallsOfIvy missed the part about the third approximation, so you're done.



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