You are Here: Home >< Maths

# FP2 Newton Raphson watch

1. https://goo.gl/S3bldn

3 i and ii

I have a vague idea of the first part, probably constructing some equation of a line with the info I'm given, I couldn't get it to work, perhaps I'm rusty with coordinate geometry.

ii is really weird for me though. I thought I could draw y=x and f(x) and show it staircase or cobweb to a, but f(x) is not in x=F(x) form so I can't do that. I've seen several of these types of questions where its something to do with tangents and convergence but I don't get them, I would like to know. Thanks in advance.
2. If the initial approximation and the second, with their corresponding y value where to be sketched on a graph, the line connecting these two point is very close to the tangent of the curve.
EDIT: whoops wrong chapter :/

Posted from TSR Mobile
3. (Original post by 16characterlimit)
https://goo.gl/S3bldn

3 i and ii

I have a vague idea of the first part, probably constructing some equation of a line with the info I'm given, I couldn't get it to work, perhaps I'm rusty with coordinate geometry.

ii is really weird for me though. I thought I could draw y=x and f(x) and show it staircase or cobweb to a, but f(x) is not in x=F(x) form so I can't do that. I've seen several of these types of questions where its something to do with tangents and convergence but I don't get them, I would like to know. Thanks in advance.
16Characters....
4. Part one involves replacing f(x+e) with its first degree Taylor expansion, which gives f(X) +f,(X)e is approximately 0

Posted from TSR Mobile
5. (Original post by drandy76)
If the initial approximation and the second, with their corresponding y value where to be sketched on a graph, the line connecting these two point is very close to the tangent of the curve.

Posted from TSR Mobile
I'm not sure I get what you mean.

Draw a tangent at (x2, f(x2) ) and it gets very close to a ?

That seems to make sense, but I don't know if that's what you meant.
6. (Original post by 16characterlimit)
I'm not sure I get what you mean.

Draw a tangent at (x2, f(x2) ) and it gets very close to a ?

That seems to make sense, but I don't know if that's what you meant.
Sorry I was thinking of the approximations and errors chapter, I'm not sure if this still applies to Newton-raphson, but yeah that's what I meant

Posted from TSR Mobile
7. (Original post by 16characterlimit)
..
Sorry, a bit busy so can't give a proper explanation, but reading through this and this might help.
8. (Original post by Zacken)
Sorry, a bit busy so can't give a proper explanation, but reading through this and this might help.
Thank you, was useful for my understanding however Taylor series aren't in the spec so I don't know how OCR would want me to answer.

https://goo.gl/YseIKK

9. (Original post by 16characterlimit)
Thank you, was useful for my understanding however Taylor series aren't in the spec so I don't know how OCR would want me to answer.

https://goo.gl/YseIKK

I didn't want you to look at the taylor series part, scroll down a few pages and look at the "geometric derivation part" - that applies to both PDF's, there's a useful picture in the second link!
10. (Original post by 16characterlimit)

That would be for part (i), which is basically just the difference in y-values f(x_1) - 0 over the change in the x value x_2 - x_1, etc...
11. (Original post by Zacken)
I didn't want you to look at the taylor series part, scroll down a few pages and look at the "geometric derivation part" - that applies to both PDF's, there's a useful picture in the second link!
Thank you! That's ii down.
12. (Original post by 16characterlimit)
Thank you! That's ii down.
Do you still need help with (i)?
13. (Original post by 16characterlimit)
Thank you, was useful for my understanding however Taylor series aren't in the spec so I don't know how OCR would want me to answer.

https://goo.gl/YseIKK

I think I misread that actually, taylor series is how you establish the general formula, not how you use it as an iterative one

Posted from TSR Mobile
14. (Original post by drandy76)
I think I misread that actually, taylor series is how you establish the general formula, not how you use it as an iterative one

Posted from TSR Mobile
The general formula is the iterative one, you derive them using the Taylor series.
15. (Original post by Zacken)
The general formula is the iterative one, you derive them using the Taylor series.
Ugh, doesn't appear to be my day today, at least I got to nab some extra notes for fp2 so it's not all bad

Posted from TSR Mobile
16. (Original post by drandy76)
Ugh, doesn't appear to be my day today, at least I got to nab some extra notes for fp2 so it's not all bad

Posted from TSR Mobile
I know the feeling. Bright side looks good, Yay!
17. Yeah I still am confused about i.
18. (Original post by 16characterlimit)
Yeah I still am confused about i.
Okay, so you can see that the tangent on the diagram. Find it's gradient. You know two of the points on the tangent,

You with me so far?

But the gradient of the tangent at is the derivative of the curve evaluated at , no? You with me?

So: You cool with me here?

Now re-arrange.
19. (Original post by Zacken)
Okay, so you can see that the tangent on the diagram. Find it's gradient. You know two of the points on the tangent,

You with me so far?

But the gradient of the tangent at is the derivative of the curve evaluated at , no? You with me?

So: You cool with me here?

Now re-arrange.
Once again thank you very much.
20. (Original post by 16characterlimit)
Once again thank you very much.
No problemo!

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 2, 2016
Today on TSR

### Results day under a month away

How are you feeling?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams