VCE Specialist 3/4 Question Thread!

[lzxnl]

I'd hope not in an exam. The fact is, I was asked that question and that's all I can really say.

Personally, I'd be looking for those, graph trends as x becomes small or large as well...those can really help and in the case of xe^x, aren't always obvious.

[IndefatigableLover]

A proof LOL



So I've gotten to the point where I've re-written the left hand side into:



But I'm unsure on what to do from there...

[lzxnl]

[Bestie]

yup, thank you

I was also wondering how would i solve:
sin(tan^-1(3/4)) how would i solve that?
does sin(tan^-1(x)) simplfy to something?

[Zealous]

yup, thank you

I was also wondering how would i solve:
sin(tan^-1(3/4)) how would i solve that?
does sin(tan^-1(x)) simplfy to something?

[Bestie]

thank you i got it

i was wondering is this correct step wise?
integral [² ₁ 1/(2x)^(1/2) dx]
[4x^(1/2)]²₁
4squreroot(2) - 4?

[IndefatigableLover]

Forgive me for asking but why did you multiply     with    in your second line? Or rather why is it allowed in this case?

[keltingmeith]

S/he did it to get the end result. Perfectly reasonable, because it's just multiplying by 1. One of those pesky things you just need to "see".

Cos^2 = 1 - sin^2, which is a difference of two squares, explaining why this method was chosen.

[IndefatigableLover]

S/he did it to get the end result. Perfectly reasonable, because it's just multiplying by 1. One of those pesky things you just need to "see".

Cos^2 = 1 - sin^2, which is a difference of two squares, explaining why this method was chosen.

Ah okay I understand how all the other steps work apart from the 2nd one but in general if I was 'stuck' (as I was in this case) then I would just essentially multiply the whole thing by '1' and hope for the best? I dunno I haven't been taught about this yet so I'm kind of confused about it that's all...

[keltingmeith]

Proofs are... Different. There's no real trick to proofs, y'see. The way it works in high school, is you start from the LHS, and need to get to the RHS in some manner. This isn't really maths, but it's high school, so just go with it. In this case, multiplying by one works. In the real world, you need to apply theorems and logic to get a result a proof.

[kinslayer]

Ah okay I understand how all the other steps work apart from the 2nd one but in general if I was 'stuck' (as I was in this case) then I would just essentially multiply the whole thing by '1' and hope for the best? I dunno I haven't been taught about this yet so I'm kind of confused about it that's all...

Adding zero and multiplying by one are often useful things to do with fractions. As an example if you multiply top and bottom of a ratio of complex numbers by the conjugate of the denominator, the result will be in the form a + bi. Adding zero to the numerator of a rational function is a good shorthand to polynomial long division in some cases.

Example of adding zero:



(another) Example of multiplying by one:



Overall a good thing to have in your toolkit. Multiplying by 1 also can help with fractions with radicals, for integration etc.

[IndefatigableLover]

Proofs are... Different. There's no real trick to proofs, y'see. The way it works in high school, is you start from the LHS, and need to get to the RHS in some manner. This isn't really maths, but it's high school, so just go with it. In this case, multiplying by one works. In the real world, you need to apply theorems and logic to get a result a proof.

Haha yeah I know there's no trick to proofs so I'm trying to get the hang of them now but that's the only one that's stumped me so far >.< But thanks again EulerFan101

Adding zero and multiplying by one are often useful things to do with fractions. As an example if you multiply top and bottom of a ratio of complex numbers by the conjugate of the denominator, the result will be in the form a + bi. Adding zero to the numerator of a rational function is a good shorthand to polynomial long division in some cases.

Example of adding zero:



(another) Example of multiplying by one:



Overall a good thing to have in your toolkit. Multiplying by 1 also can help with fractions with radicals, for integration etc.

Ooh so it not only works with just multiplying by one but also adding zero.. nice! I guess you learn something new everyday
Thanks kinslayer!

[alchemy]

A proof LOL



So I've gotten to the point where I've re-written the left hand side into:



But I'm unsure on what to do from there...

Here's an alternative method to lzxnl's if you didn't quite understand that:

1/cos(x) + sin(x)/cos(x)
= (cos(x) + cos(x)sin(x)) / cos^2(x)
= cos(x)(1+sin(x)) / (1-sin^2(x))              --> using the identity of sin^2(x) + cos^2(x) = 1.
= (cos(x) (1+sin(x)) / (1+sin(x) * (1-sin(x))
= cos(x)/(1-sin(x))

[lzxnl]

Only thing is, you've still multiplied by 1 there, this time by cos x / cos x
So it's not much different to my working xP

[alchemy]

Only thing is, you've still multiplied by 1 there, this time by cos x / cos x
So it's not much different to my working xP

Yeah i know it's essentially the same (:
But since he was confused about why you multiplied by (1-sinx)/(1-sinx) I thought I'd just say that he could've just added both fractions and taken an approach he probably was already familiar with.