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

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HeroBest ResponseYou've already chosen the best response.2
Are you going to try it or not?
 one year ago

mathmateBest ResponseYou've already chosen the best response.0
@Hero , why don't you try it, is there a problem?
 one year ago

HeroBest 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.
 one year ago

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

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

HeroBest 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.
 one year ago

mathmateBest 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?
 one year ago

HeroBest ResponseYou've already chosen the best response.2
I have to warn you though.... Challenges are usually not "easy"
 one year ago

mathmateBest ResponseYou've already chosen the best response.0
Why start with 10 pi, so far from the roots?
 one year ago

HeroBest 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
 one year ago

HeroBest ResponseYou've already chosen the best response.2
Because that's part of the "challenge" of course.
 one year ago

mathmateBest 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! :)
 one year ago

HeroBest 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.
 one year ago

mathmateBest ResponseYou've already chosen the best response.0
Hey, everything is close when compared to infinity!
 one year ago

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

HeroBest ResponseYou've already chosen the best response.2
Right now, you're just teasing
 one year ago

mathmateBest ResponseYou've already chosen the best response.0
Just wanted to find out what you're after! I'll be back.
 one year ago

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

HeroBest ResponseYou've already chosen the best response.2
@asnaseer, you're more than welcome to contribute
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
1.8955 is what I get (approx)
 one year ago

HeroBest ResponseYou've already chosen the best response.2
See what I mean @mathmate
 one year ago

HeroBest ResponseYou've already chosen the best response.2
What tool did you use to calculate it?
 one year ago

asnaseerBest 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
 one year ago

HeroBest ResponseYou've already chosen the best response.2
Wow, only 13 iterations is impressive.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
well  wolf did most of the hard slog here :)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
sorry  it took 12 iterations not 13 :)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
for 4 decimal place accuracy that is
 one year ago

HeroBest 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.
 one year ago

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

asnaseerBest ResponseYou've already chosen the best response.1
I assume TINspire is some sort of scientific calculator?
 one year ago

HeroBest ResponseYou've already chosen the best response.2
You don't know what TINspire is?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
I have a Mac  why would I also need a calculator?
 one year ago

HeroBest 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.
 one year ago

asnaseerBest 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. :)
 one year ago

HeroBest 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.
 one year ago

asnaseerBest 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?
 one year ago

HeroBest 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.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
there seem to be lots of variants  is there a particular model that ou would recommend?
 one year ago

HeroBest ResponseYou've already chosen the best response.2
The latest model. TINspire CAS models. CX is the latest version
 one year ago

HeroBest 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.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
and where do I get this software from?
 one year ago

HeroBest 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.
 one year ago

HeroBest ResponseYou've already chosen the best response.2
Are you using the Mac or Windows at the moment?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
I use both  but I am on the Mac at the moment
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
thanks Hero  greatly appreciated! :)
 one year ago

HeroBest ResponseYou've already chosen the best response.2
The homepage of the site is simply ti.com
 one year ago

HeroBest 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.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
us old fogeys don't always keep up with the latest gadgets! :D
 one year ago
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