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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. \[f(x) = \frac{1}{2} + \frac{x^2}{4} - x \sin(x) - \frac{\cos(2x)}{2}\]

Mathematics
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<--i hate math
Are you going to try it or not?
nope. no idea

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Other answers:

@Hero , why don't you try it, is there a problem?
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.
I'm pretty sure this isn't the first time you've seen users post "challenges"
Oh, I see!
It probably will converge, but to which root? Are you looking for a particular one?
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.
So you want us to blindly find a root, and you don't care which of the three we give you?
I have to warn you though.... Challenges are usually not "easy"
Why start with 10 pi, so far from the roots?
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
Because that's part of the "challenge" of course.
I call it blindly when we don't have any judgment to make, or stick to our preferences! :)
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.
Hey, everything is close when compared to infinity!
Okay, so are you going to solve this challenge or not?
Right now, you're just teasing
Just wanted to find out what you're after! I'll be back.
Well, you better hurry up before someone else figures it out! lol
:)
@asnaseer, you're more than welcome to contribute
-1.8955 is what I get (approx)
See what I mean @mathmate
in 13 iterations
Impressive.
What tool did you use to calculate it?
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
until it converged
Wow, only 13 iterations is impressive.
well - wolf did most of the hard slog here :)
I did it in less than 13
sorry - it took 12 iterations not 13 :)
for 4 decimal place accuracy that is
Funny thing is, if you use mathematica, maple, or any ready-made program to do it, it will say that it doesn't converge.
I did it using TI-Nspire in the same manual manner as you and got it.
I assume TI-Nspire is some sort of scientific calculator?
You don't know what TI-Nspire is?
nope :)
You should look it up
I have a Mac - why would I also need a calculator?
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.
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. :)
Good for you. Maybe you can look into it for your kids who might want one some day.
good point - I will - I guess from the manner in which you are promoting it, it must be a good calculator?
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.
there seem to be lots of variants - is there a particular model that ou would recommend?
The latest model. TI-Nspire CAS models. CX is the latest version
But I would recommend you try out the student software just to get the hang of the usage.
this one? http://www.amazon.co.uk/Texas-Instruments-Graphic-Calculator-Science/dp/B0052RU8TO/ref=sr_1_1?ie=UTF8&qid=1347150004&sr=8-1
and where do I get this software from?
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.
yes please
Are you using the Mac or Windows at the moment?
I use both - but I am on the Mac at the moment
http://education.ti.com/calculators/downloads/US/Software/Download/en/6770/8184/TI-Nspire_CAS_Student_Software-3.2.0.1219.zip
thanks Hero - greatly appreciated! :)
The homepage of the site is simply ti.com
ok
It's the best calculator ever, that's why I'm surprised you never heard of it.
us old fogeys don't always keep up with the latest gadgets! :D
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