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# Year 13 Maths Help Thread

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1. Would the following problem be accessible for a C4 student?

Find the total area between the curves (measured positively) and its inverse function from to and from to .
2. (Original post by Palette)
Would the following problem be accessible for a C4 student?

Find the total area enclosed by the curves (measured positively) and its inverse function from to and from to .
Wording is weird... can you make it clearer?
3. (Original post by RDKGames)
Wording is weird... can you make it clearer?
I could rephrase it as 'Find the area between the graphs of sin x and arcsin x between x=-1 and x=0. Then find the area between the graphs of sin x and arcsin x between x=0 and x=1. What is the sum of these two areas?'
4. (Original post by Palette)
I could rephrase it as 'Find the area between the graphs of sin x and arcsin x between x=-1 and x=0. Then find the area between the graphs of sin x and arcsin x between x=0 and x=1. What is the sum of these two areas?'
You mean this?

5. (Original post by RDKGames)
You mean this?

Yes.
6. (Original post by Palette)
Yes.
Just rephrase it to

I'm unsure if C4 integrates arcsine, but it's in the formula booklet anyway so it's doable.

Update: Yes it's doable. Basic inverse trig integration is covered in C3
7. (Original post by RDKGames)
I'm unsure if C4 integrates arcsine, but it's in the formula booklet anyway so it's doable.

You're getting confused with differentiation and integration. The way to integrate these is to use IBP with and .
8. (Original post by Zacken)
You're getting confused with differentiation and integration. The way to integrate these is to use IBP with and .
Yeah I wasn't sure if it's integration or differentiation that is given to you in the formula booklet, still there so students can figure it out I'm sure.
9. Proving various trigonometric identities is by far my weakest point in C3.

How can I start proving that ?
10. (Original post by Palette)
Proving various trigonometric identities is by far my weakest point in C3.

How can I start proving that ?
The obvious way; convert everything to sines and cosines first off: , then well, everybody should be seeing that we want so the only sensible plan of attack is to use and in the numerator and denominator respectively, for two obvious reasons:

(i) It gets in the numerator and in the denominator; which is the form for .

(ii) It gets rid of the pesky so the division becomes straightforward.

Anywho, that gets you
11. (Original post by Zacken)
The obvious way; convert everything to sines and cosines first off: , then well, everybody should be seeing that we want so the only sensible plan of attack is to use and in the numerator and denominator respectively, for two obvious reasons:
Everybody except me I suppose. I was thinking too much along the lines of the half angle formulae when I saw .
(i) It gets in the numerator and in the denominator; which is the form for .

(ii) It gets rid of the pesky so the division becomes straightforward.

Anywho, that gets you
Thanks for the help!
12. M3 question:
Is there a way that I can visualise in my head? I know it means 'the rate of change of velocity with respect to displacement' but it still feels a bit strange when all the questions in mechanics so far are to do with '_____ with respect to time'.
13. (Original post by Palette)
M3 question:
Is there a way that I can visualise in my head? I know it means 'the rate of change of velocity with respect to displacement' but it still feels a bit strange when all the questions in mechanics so far are to do with '_____ with respect to time'.
Just write it as .
14. I am currently studying the mean value theorem, a piece of calculus that is taught in schools in the US but not in the UK.

I wanted to know some results that can be derived from the mean value theorem and one of them happens to be:

If is differentiable and for all , then is constant.

I am confused by what means.

15. (Original post by Palette)
I am currently studying the mean value theorem, a piece of calculus that is taught in schools in the US but not in the UK.

I wanted to know some results that can be derived from the mean value theorem and one of them happens to be:

If is differentiable and for all , then is constant.

I am confused by .
It's a function of 2 variables, a and b. (I believe).
16. (Original post by Palette)
I am confused by what means.
Wow, where did you get that from? That's a horrible abuse of notation. It should be: the function is differentiable, etc... i.e: the domain of is and the co-domain is .
17. (Original post by Zacken)
Wow, where did you get that from? That's a horrible abuse of notation. It should be: the function is differentiable, etc... i.e: the domain of is and the co-domain is .
The TeX messed up when I was copying and pasting it. Was in a rush so I didn't have my TeX sheet with me. I can show you the source- it looks fine there:

http://math.stackexchange.com/questi...-value-theorem

It must have been TSR as I copied directly from the TeX source in the link above. Even had I spotted it, I wouldn't have known about the distinction between and as I'd have thought that they were as interchangeable as and .

Please forgive my numerous mathematical heresies over the past year.
18. (Original post by Palette)
I'd have thought that they were as interchangeable as and .
Those aren't interchangeable.
19. (Original post by Zacken)
Those aren't interchangeable.
My C3 textbook states:

You can write functions in two different ways: and .

Is the textbook misleading or am I making some classic mistake in analysis?

P.S. I now understand why the TeX went wrong. I now remember that there were initially spacing issues with the TeX when I first copied it so I had to retype parts. Hence \mathbb{R} was accidentally typed as \mathbb(R) and the colon was left out in f: (a, b) as I was rushing it. I think that explains it!
20. (Original post by Palette)
My C3 textbook states:

You can write functions in two different ways: and .

Is the textbook misleading or am I making some classic mistake in analysis?

P.S. I now understand why the TeX went wrong. I now remember that there were initially spacing issues with the TeX when I first copied it so I had to retype parts. Hence \mathbb{R} was accidentally typed as \mathbb(R) and the colon was left out in f: (a, b) as I was rushing it. I think that explains it!
You can write a function like this

.
As you can see the function is defined completely, you have the domain, codomain and the mapping.
You won't see it at A-level but it can be quite important to have all these terms defined for a function.
For example if we have

This is different to the function

.

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