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

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lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
<i hate math
 2 years ago

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

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
nope. no idea
 2 years ago

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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.
 2 years ago

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

mathmate Group TitleBest ResponseYou've already chosen the best response.0
Oh, I see!
 2 years ago

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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.
 2 years ago

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

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

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.2
Because that's part of the "challenge" of course.
 2 years ago

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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.
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.0
Hey, everything is close when compared to infinity!
 2 years ago

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

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

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

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

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

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
1.8955 is what I get (approx)
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.2
See what I mean @mathmate
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
in 13 iterations
 2 years ago

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

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
I 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
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
until it converged
 2 years ago

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

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
I did it in less than 13
 2 years ago

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

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

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

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

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

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
You should look it up
 2 years ago

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
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. :)
 2 years ago

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

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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.
 2 years ago

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

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

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

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

Hero Group TitleBest ResponseYou've already chosen the best response.2
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.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yes please
 2 years ago

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

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

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

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

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

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