Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ksaimouli Group Title

estimate roots newtons linearization

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353960049993:dw|

    • 2 years ago
  2. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Is this what you mean http://en.wikipedia.org/wiki/Newton's_method

    • 2 years ago
  3. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • 2 years ago
  4. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If you define a function f(x)= x^2-5 it will have a zero when x is sqrt(5) You can use Newton's method to find that zero (x value) \[ x_{n+1}= x_n - \frac{f(x_n)}{f'(x_n)} \]

    • 2 years ago
  5. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    can you find f'(x) ?

    • 2 years ago
  6. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but i need the estimation of root5 i think ur r thinking other one

    • 2 years ago
  7. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Maybe you mean a taylor series approximation? f(x) ~ f(a) + f'(a)(x-a)

    • 2 years ago
  8. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm yup

    • 2 years ago
  9. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I would pick a=4 because you know the square root of 4

    • 2 years ago
  10. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    exactly the same

    • 2 years ago
  11. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ohk

    • 2 years ago
  12. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    here f(x)= \(x^{\frac{1}{2}}\) \[ f'(x)= \frac{1}{2}x^{-1/2} \] evaluate this at x= a = 4

    • 2 years ago
  13. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353961871007:dw|

    • 2 years ago
  14. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, so your approximate function is f(x) = 2 + (1/4)*(x-4) reasonable for x values near 4

    • 2 years ago
  15. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how did u get 2 u said 4

    • 2 years ago
  16. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you start with f(x) ~ f(a) + f'(a) (x-a) f(x)= sqrt(x) with a=4, f(a) is sqrt(4)

    • 2 years ago
  17. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

    • 2 years ago
  18. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353962194869:dw|

    • 2 years ago
  19. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the question asks for sqrt(5) , so plug in 5 for x into your estimation equation

    • 2 years ago
  20. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    2.25

    • 2 years ago
  21. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, and 2.25^2 is 5.0625 which is pretty close to 5

    • 2 years ago
  22. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    got u one small doubt what if it is root31 shall i pick root36 or root25

    • 2 years ago
  23. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    pick the closer one. 31 is in the middle, so either end will not be very accurate.

    • 2 years ago
  24. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    root30 but this is not perfect square

    • 2 years ago
  25. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    30 is not a perfect square. so you want to pick a nearby "a" where you know the root. 25 is the closest square. 36 is almost as close. Using 25 is probably better by a little bit that using 36

    • 2 years ago
  26. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    not to butt in but newton's method in this case is identical to mechanics rule

    • 2 years ago
  27. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I never heard of Professor Mechanic

    • 2 years ago
  28. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    you can use \[x_{n+1}=\frac{1}{2}\left (x_n+\frac{5}{x_n}\right)\]

    • 2 years ago
  29. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    mechanic predated newton in fact i think mechanic was babylonian, maybe circa 3000 BC it is an old method for finding roots, but if you do the algebra with newtons method for square roots it ends up being the same. the recursion to find \(\sqrt{a}\) is \[x_{n+1}=\frac{1}{2}\left (x_n+\frac{a}{x_n}\right)\]

    • 2 years ago
  30. phi Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    es, for f(x)= x^2 -a and f'(x)= 2x newton's x- f(x)/f'(x) is x - (x^2-a)/2x = (2x^2 -x^2 +a)/2x which becomes mechanic with a few more steps

    • 2 years ago
  31. ksaimouli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks all

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.