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

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Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Are you going to try it or not?

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0@Hero , why don't you try it, is there a problem?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2I 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
 2 years ago
Best ResponseYou've already chosen the best response.2I'm pretty sure this isn't the first time you've seen users post "challenges"

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0It probably will converge, but to which root? Are you looking for a particular one?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2All 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
 2 years ago
Best ResponseYou've already chosen the best response.0So you want us to blindly find a root, and you don't care which of the three we give you?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2I have to warn you though.... Challenges are usually not "easy"

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0Why start with 10 pi, so far from the roots?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Not "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
 2 years ago
Best ResponseYou've already chosen the best response.2Because that's part of the "challenge" of course.

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0I call it blindly when we don't have any judgment to make, or stick to our preferences! :)

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2The 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
 2 years ago
Best ResponseYou've already chosen the best response.0Hey, everything is close when compared to infinity!

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Okay, so are you going to solve this challenge or not?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Right now, you're just teasing

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0Just wanted to find out what you're after! I'll be back.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Well, you better hurry up before someone else figures it out! lol

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2@asnaseer, you're more than welcome to contribute

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.11.8955 is what I get (approx)

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2What tool did you use to calculate it?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1I calculates the derivative, then plugged it into the NewtonRaphson equation and entered that into Wolfram as this: http://www.wolframalpha.com/input/?i=y%3Dx%2B%281%2Bx^2%2F22*x*sin%28x%29cos%282x%29%29%2F%28x2sin%28x%29%29%282cos%28x%291%29+for+x%3D10pi this gave a value for y, which I then plugged back into x in wolfram and continued this iteration

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Wow, only 13 iterations is impressive.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1well  wolf did most of the hard slog here :)

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1sorry  it took 12 iterations not 13 :)

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1for 4 decimal place accuracy that is

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Funny thing is, if you use mathematica, maple, or any readymade program to do it, it will say that it doesn't converge.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2I did it using TINspire in the same manual manner as you and got it.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1I assume TINspire is some sort of scientific calculator?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2You don't know what TINspire is?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1I have a Mac  why would I also need a calculator?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Well, 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
 2 years ago
Best ResponseYou've already chosen the best response.1I 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
 2 years ago
Best ResponseYou've already chosen the best response.2Good for you. Maybe you can look into it for your kids who might want one some day.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1good point  I will  I guess from the manner in which you are promoting it, it must be a good calculator?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2I 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
 2 years ago
Best ResponseYou've already chosen the best response.1there seem to be lots of variants  is there a particular model that ou would recommend?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2The latest model. TINspire CAS models. CX is the latest version

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2But I would recommend you try out the student software just to get the hang of the usage.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1and where do I get this software from?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah, 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.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2Are you using the Mac or Windows at the moment?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1I use both  but I am on the Mac at the moment

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1thanks Hero  greatly appreciated! :)

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2The homepage of the site is simply ti.com

Hero
 2 years ago
Best ResponseYou've already chosen the best response.2It's the best calculator ever, that's why I'm surprised you never heard of it.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1us old fogeys don't always keep up with the latest gadgets! :D
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