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# Newton-Raphson watch

1. f(x) = 0.25x – 2 + 4 (sinx)^1/2

The equation f(x) = 0 also has a root beta between x = 10.75 and x = 11.25.

(c) Taking 11 as a first approximation to beta , use the Newton-Raphson process on f(x) once to
obtain a second approximation to beta. Give your answer to 2 decimal places.

The problem I am having is finding the differential of f(x).

It is 0.25 + 2cosx/(sinx)^1/2 right??

The thing is, it doesn't work. ALSO with numerical methods, are you in radians or degrees, obviously as this question has trig functions, being in degrees can mean a completely different from when you're in radians.
2. In this case you diff. term by term, so you would get:

f'(x) = 0.25 + 4cos(x)

HTH

3. (Original post by + polarity -)
In this case you diff. term by term, so you would get:

f'(x) = 0.25 + 4cos(x)

HTH

Forgive me, I just edited it, it's actually 4(sinx)^1/2 that I meant, haha I wouldn't ever be that sleepy and miss the differential of sinx like that. Also, what does HTH mean, as well as that, why do you think radians, or is that a hunch?
4. Oh...

okay, with (sinx)1/2 you'd need to use the chain rule I think.

u = sinx, so "y" = u1/2

du/dx = cosx, and dy/du = 1/2 u-1/2

dy/dx = dy/du · du/dx = 1/2 u-1/2 · cosx = 1/2 cosx·sinx-1/2 or 1/2 cosx/sinx1/2

Then you can put that back into the main thing, so f'(x) = 0.25 + 2cosx·sinx-1/2

HTH means hope that helps , and in most questions involving calculus and trig. functions, the limits tended to be in radians, so it's an educated guess.
5. (Original post by + polarity -)
In this case you diff. term by term, so you would get:

f'(x) = 0.25 + 4cos(x)

HTH

Actually, it's cool now, I've got the differential I needed, thanks anyway!
6. (Original post by Clarity Incognito)
Actually, it's cool now, I've got the differential I needed, thanks anyway!
Oh come on, it took me ages to bash that all out!
7. (Original post by + polarity -)
Oh...

okay, with (sinx)1/2 you'd need to use the chain rule I think.

u = sinx, so "y" = u1/2

du/dx = cosx, and dy/du = 1/2 u-1/2

dy/dx = dy/du · du/dx = 1/2 u-1/2 · cosx = 1/2 cosx·sinx-1/2 or 1/2 cosx/sinx1/2

Then you can put that back into the main thing, so f'(x) = 0.25 + 2cosx·sinx-1/2

HTH means hope that helps , and in most questions involving calculus and trig. functions, the limits tended to be in radians, so it's an educated guess.
Haha, lolol, sorry, there has been a lot of confusion here. All I can say is thank you for helping despite my inadequacies in actually posting the real question. I have it sorted now, a tiny error I have found. Ok, thanks I'll tell you if I verify that little radians conjecture you have.
8. Okay.
9. (Original post by + polarity -)
Oh come on, it took me ages to bash that all out!
Haha, I keep taking too long to reply that you reply again. Essentially, I did the same differentiation as you did but I was meant to do the differential of 4sin(x^1/2) which I was getting confused with 4(sinx)^1/2. You love maths though so it was in the name of fun? Also, if you're looking for rep, my rep power is worth less than the copper on a penny. Someone unknown took it upon themselves to deliver sweet retribution upon me.
10. (Original post by + polarity -)
Okay.
I feel bad now! What type of maths are you doing these days btw?
11. (Original post by Clarity Incognito)
I feel bad now! What type of maths are you doing these days btw?
Engineering Maths. I don't feel bad for not doing A2 Further Maths because I've covered several large chunks of it this semester.
12. (Original post by + polarity -)
Engineering Maths. I don't feel bad for not doing A2 Further Maths because I've covered several large chunks of it this semester.
Epic, yeah, where at? My friend does biochem at warwick and they made him learn A level maths as quick as possible. It is rather handy nonetheless to have under your belt. Why the applied maths... !
13. (Original post by Clarity Incognito)
Epic, yeah, where at? My friend does biochem at warwick and they made him learn A level maths as quick as possible. It is rather handy nonetheless to have under your belt. Why the applied maths... !
Bristol.

I did as many Mechanics modules as I could (M1-3, then M4 & 5 casual lessons ), and I've had to apply what I learnt from M1-3 so far. So I think the applied modules are useful.
14. (Original post by Clarity Incognito)
Haha, I keep taking too long to reply that you reply again. Essentially, I did the same differentiation as you did but I was meant to do the differential of 4sin(x^1/2) which I was getting confused with 4(sinx)^1/2. You love maths though so it was in the name of fun? Also, if you're looking for rep, my rep power is worth less than the copper on a penny. Someone unknown took it upon themselves to deliver sweet retribution upon me.
It's fine; I'm not motivated by rep.
15. (Original post by + polarity -)
Bristol.

I did as many Mechanics modules as I could (M1-3, then M4 & 5 casual lessons ), and I've had to apply what I learnt from M1-3 so far. So I think the applied modules are useful.
Haha, I could totally come and actually meet you next year but I wouldn't want to taint my pure maths modules I kid I kid, and also because I don't know where I want to go yet but yeah, it wasn't really a question of utility, just one of purity, I may even go as far as to say it was rhetorical
16. (Original post by Clarity Incognito)
Haha, I could totally come and actually meet you next year but I wouldn't want to taint my pure maths modules I kid I kid, and also because I don't know where I want to go yet but yeah, it wasn't really a question of utility, just one of purity, I may even go as far as to say it was rhetorical
Oh, I see. Another question I was tricked into answering.
17. (Original post by + polarity -)
Oh, I see. Another question I was tricked into answering.
I fear it was not my chicanery as a trickster that has led to your misfortunes on this thread, I might even suggest that it were just that time of morning! What the hell ARE you doing at this time?
18. (Original post by Clarity Incognito)
I fear it was not my chicanery as a trickster that has led to your misfortunes on this thread, I might even suggest that it were just that time of morning! What the hell ARE you doing at this time?
I am nocturnal. The more I try to make my sleeping pattern more normal, the worse it gets.
19. (Original post by + polarity -)
I am nocturnal. The more I try to make my sleeping pattern more normal, the worse it gets.
Well, I cannot keep up I'm afraid, enjoy your nocturnal practices, I'll see you later! Good morning!
20. (Original post by Clarity Incognito)
Well, I cannot keep up I'm afraid, enjoy your nocturnal practices, I'll see you later! Good morning!
Goodbye, CI.

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