Hero
  • Hero
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
lgbasallote
  • lgbasallote
<--i hate math
Hero
  • Hero
Are you going to try it or not?
lgbasallote
  • lgbasallote
nope. no idea

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