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Pixelfairy #1
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#21
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#21
(Original post by Bezza)
Seeing as it's only p2, this won't really help, but if you use the newton-raphson method, and starting values of 1 and 3, you find that the roots are about 3.066 and 1.691, so N can be 1 and 3. I can't remember how they'd expect you do find this in p2 though!
I'm doing P2 and the iterative method is at the very end of the book

Anyways I got 0 and 3 as the answers for N (which are correct at the back of the book).

If you want to see what i did, http://www.pixelfairies.co.uk/img023.jpg :cool:
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Bezza
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#22
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(Original post by MyNameIsNeo)
I think you got the decimal point in the wrong place! 0.1691 not 1.691.
:eek: Not another mistake - that's 2 in a minute! 0.1691 was what I meant
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Bezza
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#23
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(Original post by Pixelfairy #1)
I'm doing P2 and the iterative method is at the very end of the book

Anyways I got 0 and 3 as the answers for N (which are correct at the back of the book).

If you want to see what i did, http://www.pixelfairies.co.uk/img023.jpg :cool:
That's probably the way they were expecting you to do it, since the method i used is p5 or 6! You should really substitute back into the equation to check you have got the right values of N and that the formula doesn't go to a completely different number after a few more iterations. To do this, substitute both values of N and N+1 into e^x - 7x, you should get N negative and N+1 positive (or the other way round), so you know that between x=N and N+1, the expression equals zero, because there are no asymptotes in the function. They often expect you to do this for a mark or 2, so you need to write it down.
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Pixelfairy #1
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#24
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(Original post by Bezza)
That's probably the way they were expecting you to do it, since the method i used is p5 or 6! You should really substitute back into the equation to check you have got the right values of N and that the formula doesn't go to a completely different number after a few more iterations. To do this, substitute both values of N and N+1 into e^x - 7x, you should get N negative and N+1 positive (or the other way round), so you know that between x=N and N+1, the expression equals zero, because there are no asymptotes in the function. They often expect you to do this for a mark or 2, so you need to write it down.
Good point... I never thought of checking it! :rolleyes:
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Bezza
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(Original post by Pixelfairy #1)
Good point... I never thought of checking it! :rolleyes:
It's quite important really because you never know what's gonna happen with iteration formulae, sometimes they go mad after loads of iterations so you wouldn't know. You have to do the same kind of check to show you're right to a certain number of decimal places, say 1.23, sub in 1.225 and 1.235, and say you get a zero between them.
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MyNameIsNeo
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#26
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Do a little sketch - it will help you keep track of what you are doing.
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Pixelfairy #1
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#27
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#27
(Original post by Bezza)
It's quite important really because you never know what's gonna happen with iteration formulae, sometimes they go mad after loads of iterations so you wouldn't know. You have to do the same kind of check to show you're right to a certain number of decimal places, say 1.23, sub in 1.225 and 1.235, and say you get a zero between them.
Yeah I've seen exam questions that ask you to prove that it's correct to 3sf or 4 dp or whatever. Do they expect you to check in the exam even if they don't ask it as a question?
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Fermat
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#28
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#28
(Original post by pinkfairy)
Anyone help on this one?:

A root of the equation e^x-7x=0 lies in the interval N<x<N+1 where N is an integer. Find 2 values for N.

I'm stuck! Please help! Love Pinkfairy xxx
I don't think you have to use iteration methods
The question simply asks you to find an integer range in which a root lies.

let y=e^x - 7x

Now just make a little table.
Write down integer values for x, say starting at x=0, and increment by 1.
Write down the corresponding values of y.
When y changes sign - then you've got a root - and you've also got the integer range that it happens in.

I get roots in [0,1] and [3,4]
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Bezza
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#29
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(Original post by Pixelfairy #1)
Yeah I've seen exam questions that ask you to prove that it's correct to 3sf or 4 dp or whatever. Do they expect you to check in the exam even if they don't ask it as a question?
They probably will expect you to do this whether it asks or not, so if it just says find to 3dp, you have to check you're correct, because although your iteration gives that answer, it may not necessarily be the right iteration or the right answer. I do edexcel and we're always told to do it by our pure teacher. I think it sometimes just says prove it as a reminder. Sometimes they'll also say "Prove there is a root between .. and ..", or "at ... to 3dp", and you use the same method to prove this.
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pinkfairy
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#30
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Thank you all for your help! Love Pinkfairy xxx
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