## Hero Group Title Challenge: Use Newton's Method to approximate the zero of the following function using $$10 \pi$$ as the initial value. And yes, it DOES coverge. $f(x) = \frac{1}{2} + \frac{x^2}{4} - x \sin(x) - \frac{\cos(2x)}{2}$ one year ago one year ago

1. lgbasallote Group Title

<--i hate math

2. Hero Group Title

Are you going to try it or not?

3. lgbasallote Group Title

nope. no idea

4. mathmate Group Title

@Hero , why don't you try it, is there a problem?

5. Hero Group Title

I posted this as a challenge. Do you know what that means? It means I already know the answer and I'm challenging others to try it as well.

6. Hero Group Title

I'm pretty sure this isn't the first time you've seen users post "challenges"

7. mathmate Group Title

Oh, I see!

8. mathmate Group Title

It probably will converge, but to which root? Are you looking for a particular one?

9. Hero Group Title

All you have to do is use $$10 \pi$$ as the initial root and see what it converges to. When you find the number, post it on here.

10. mathmate Group Title

So you want us to blindly find a root, and you don't care which of the three we give you?

11. Hero Group Title

I have to warn you though.... Challenges are usually not "easy"

12. mathmate Group Title

Why start with 10 pi, so far from the roots?

13. Hero Group Title

Not "blindly". The only thing you need to use Newton's method are the following: 1. Newton's Formula 2. f(x) 3. f'(x) 4. The initial value

14. Hero Group Title

Because that's part of the "challenge" of course.

15. mathmate Group Title

I call it blindly when we don't have any judgment to make, or stick to our preferences! :)

16. Hero Group Title

The bit about how far $$10 \pi$$ is from the root is only relative. It is pretty close to one of the roots compared to infinity.

17. mathmate Group Title

Hey, everything is close when compared to infinity!

18. Hero Group Title

Okay, so are you going to solve this challenge or not?

19. Hero Group Title

Right now, you're just teasing

20. mathmate Group Title

Just wanted to find out what you're after! I'll be back.

21. Hero Group Title

Well, you better hurry up before someone else figures it out! lol

22. mathmate Group Title

:)

23. Hero Group Title

@asnaseer, you're more than welcome to contribute

24. asnaseer Group Title

-1.8955 is what I get (approx)

25. Hero Group Title

See what I mean @mathmate

26. asnaseer Group Title

in 13 iterations

27. Hero Group Title

Impressive.

28. Hero Group Title

What tool did you use to calculate it?

29. asnaseer Group Title

I calculates the derivative, then plugged it into the Newton-Raphson equation and entered that into Wolfram as this: http://www.wolframalpha.com/input/?i=y%3Dx%2B%281%2Bx^2%2F2-2*x*sin%28x%29-cos%282x%29%29%2F%28x-2sin%28x%29%29%282cos%28x%29-1%29+for+x%3D10pi this gave a value for y, which I then plugged back into x in wolfram and continued this iteration

30. asnaseer Group Title

until it converged

31. Hero Group Title

Wow, only 13 iterations is impressive.

32. asnaseer Group Title

well - wolf did most of the hard slog here :)

33. Hero Group Title

I did it in less than 13

34. asnaseer Group Title

sorry - it took 12 iterations not 13 :)

35. asnaseer Group Title

for 4 decimal place accuracy that is

36. Hero Group Title

Funny thing is, if you use mathematica, maple, or any ready-made program to do it, it will say that it doesn't converge.

37. Hero Group Title

I did it using TI-Nspire in the same manual manner as you and got it.

38. asnaseer Group Title

I assume TI-Nspire is some sort of scientific calculator?

39. Hero Group Title

You don't know what TI-Nspire is?

40. asnaseer Group Title

nope :)

41. Hero Group Title

You should look it up

42. asnaseer Group Title

I have a Mac - why would I also need a calculator?

43. Hero Group Title

Well, I guess if you are not still in school, it won't be of very much use to you. I just like to play around with it. Plus you can program all kinds of stuff on it.

44. asnaseer Group Title

I left school (and Uni) a loooong time ago my friend - and I use the Mac at home and a windows PC at work to program in. so I don't really need a calculator as such these days. :)

45. Hero Group Title

Good for you. Maybe you can look into it for your kids who might want one some day.

46. asnaseer Group Title

good point - I will - I guess from the manner in which you are promoting it, it must be a good calculator?

47. Hero Group Title

I don't recommend stuff that isn't impressive. I think you should at least try out the student software. It's something you can download onto your computer and play around with.

48. asnaseer Group Title

there seem to be lots of variants - is there a particular model that ou would recommend?

49. Hero Group Title

The latest model. TI-Nspire CAS models. CX is the latest version

50. Hero Group Title

But I would recommend you try out the student software just to get the hang of the usage.

51. asnaseer Group Title
52. asnaseer Group Title

and where do I get this software from?

53. Hero Group Title

Yeah, I was just about to mention that you should go to TI's site to get the software. I can post a link to that.

54. asnaseer Group Title

55. Hero Group Title

Are you using the Mac or Windows at the moment?

56. asnaseer Group Title

I use both - but I am on the Mac at the moment

57. Hero Group Title
58. asnaseer Group Title

thanks Hero - greatly appreciated! :)

59. Hero Group Title

The homepage of the site is simply ti.com

60. asnaseer Group Title

ok

61. Hero Group Title

It's the best calculator ever, that's why I'm surprised you never heard of it.

62. asnaseer Group Title

us old fogeys don't always keep up with the latest gadgets! :D