anonymous
  • anonymous
Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 8 = 0. I worked it out and got 3.6666667 but it was wrong, please help!
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
Newton's Method \[\Large x_{n+1} = x_n - \frac{f(x_n)}{f \ '(x_n)}\]
jim_thompson5910
  • jim_thompson5910
If n = 1, then \[\Large x_{n+1} = x_n - \frac{f(x_n)}{f \ '(x_n)}\] \[\Large x_{1+1} = x_1 - \frac{f(x_1)}{f \ '(x_1)}\] \[\Large x_{2} = 1 - \frac{f(1)}{f \ '(1)}\] So you need to compute both f(1) and f ' (1). Do you know how to do that?
anonymous
  • anonymous
yeah, i worked everything out i got x^4-x-8/4x^3-1 and I plugged in 1 for the x and then got -8/3, then i did 1-(-8/3) and got 3.66667?

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jim_thompson5910
  • jim_thompson5910
Yeah I'm getting that too. Maybe they want you to round a very specific way?
jim_thompson5910
  • jim_thompson5910
I doubt they want it as a fraction, but who knows really.
anonymous
  • anonymous
that's what i was thinking, that maybe they wanted it in fraction form, but it doesn't specify...
jim_thompson5910
  • jim_thompson5910
I've never seen newton's method approximations as fractions. Usually they are in decimal form. Can you post a screenshot of the full problem?
anonymous
  • anonymous
Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 8 = 0. x2 =3.67 Incorrect: Your answer is incorrect.
anonymous
  • anonymous
That's all of it
jim_thompson5910
  • jim_thompson5910
Hmm so odd and frustrating. It would be nice if they added "round to 5 decimal places" or something.
anonymous
  • anonymous
exactly! and i only have two tries so im scared to use my last one and get it wrong, since i dont know how im supposed to type the answer
jim_thompson5910
  • jim_thompson5910
The only thing you can do really is look back at previous correct problems to see what the computer wants. Or try to guess it anyway.
jim_thompson5910
  • jim_thompson5910
Or ask the teacher. I would ask for points back if you get it wrong since this problem is unfair.
anonymous
  • anonymous
yeah I'll try to do that, thanks for checking my answer though!
jim_thompson5910
  • jim_thompson5910
no problem
anonymous
  • anonymous
it was in fraction form lol
jim_thompson5910
  • jim_thompson5910
so strange, but I guess computers tend to be that way

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