Use Newton’s method with the specified initial approximation x1 to find x3.

  • Thread starter phillyolly
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  • #1
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Please verify my answer.

Homework Statement



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

Homework Equations





The Attempt at a Solution



x5+2=0, x1=-1
y'=5x4
x(n+1)=xn-(x5+2)/(5x4 )

For n=1
x2=-1-((-1)5+2)/(5(-1)4 )=-6/5=-1.2
For n=2

x3=-1.2-((-1.2)5+2)/(5(-1.2)4 )= -1.2-0.4883/10.368=-1.2+0.047=-1.1530
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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Please verify my answer.

Homework Statement



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

Homework Equations





The Attempt at a Solution



x5+2=0, x1=-1
y'=5x4
x(n+1)=xn-(x5+2)/(5x4 )
This should be
x(n+1)=xn-(xn5+2)/(5xn4 )

For n=1
x2=-1-((-1)5+2)/(5(-1)4 )=-6/5=-1.2
For n=2

x3=-1.2-((-1.2)5+2)/(5(-1.2)4 )= -1.2-0.4883/10.368=-1.2+0.047=-1.1530

Looks good, but you aren't at "4 decimal places" yet. Continue until you get two consecutive results that are the same to 4 decimal places (and I would recommend doing the calculations to at least 5 decimal places until then).
 
  • #3
157
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Hi! What do you mean by
Looks good, but you aren't at "4 decimal places" yet.
?

The task says to do the third approximation, which I found already....
Do you mean I should do the fourth...and the fifth?...
 
  • #4
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I think that HallsOfIvy missed the part about the third approximation, so you're done.
 

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