HSC 2012 MX2 Marathon (archive) (1 Viewer)

[SpiralFlex]

Re: 2012 HSC MX2 Marathon

Many methods I can't type as I am on iPhone so I will demonstrate verbally. You can us normal integration by parts then do it again. Then adding both results of the integrate something should cancel out nicely. Second method is to use Eulers formula. Or you can change it to an exponential base and introducE another variable and go from there.

 

[someth1ng]

Re: 2012 HSC MX2 Marathon

Graph: (x^2+y^2-1)^3-x^2*y^3=0

 

[Nooblet94]

Re: 2012 HSC MX2 Marathon

Patel Ex 5E Q28
"Show that the polynomial has a multiple root provided:
.
Find this root."

I've found the root, I just can't work out how to show that condition. It's pissing me off because it's the only question in the entire chapter I've been unable to do and it'll probably be something really simple that I'm missing.

 

[mnmaa]

Re: 2012 HSC MX2 Marathon

fun question to do for anyone interested-
Suppose that f(1) = 2, f(4) = 5, f '(1) = 5, f '(4) = 4, and f '' is continuous. Find the value of the following integral.

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

Patel Ex 5E Q28
"Show that the polynomial has a multiple root provided:
.
Find this root."

I've found the root, I just can't work out how to show that condition. It's pissing me off because it's the only question in the entire chapter I've been unable to do and it'll probably be something really simple that I'm missing.

Okay I got it, but its a very ugly question. Give me a moment to post up solutions.

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

Here you go. I did it in as many steps as possible so you don't miss out on anything:

 

[shaon0]

Re: 2012 HSC MX2 Marathon

8?

 

[nightweaver066]

Re: 2012 HSC MX2 Marathon

fun question to do for anyone interested-
Suppose that f(1) = 2, f(4) = 5, f '(1) = 5, f '(4) = 4, and f '' is continuous. Find the value of the following integral.

If you want to use Latex in your post, use the opening and closing brackets











Not too sure ..

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

If you want to use Latex in your post, use the opening and closing brackets











Not too sure ..

I got 8 as well.

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

You made an arithmetic error in the third line:



The second 4 shouldn't be there, it should be:

 

[Drongoski]

Re: 2012 HSC MX2 Marathon

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

You appear to have forgotten to type out the substitution limits for the:



And there appears to be a 'd' in the middle of your first integral lol.

 

[Drongoski]

Re: 2012 HSC MX2 Marathon

You appear to have forgotten to type out the substitution limits for the:



And there appears to be a 'd' in the middle of your first integral lol.

Yes I wanted to put the limits later - being a slow typist. The 'd' in the 1st integral is absolutely correct - the differential df'(x) = f''(x)dx.

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

The 'd' in the 1st integral is absolutely correct.

I do not understand how this works. Could you please explain?

 

[shaon0]

Re: 2012 HSC MX2 Marathon

d(f'(x))=∂f'/∂x dx =df'/dx dx = f"(x) dx

 

[Carrotsticks]

Re: 2012 HSC MX2 Marathon

df'(x) is the differential = f''(x)dx.

d(f'(x))=∂f'/∂x dx =df'/dx dx = f"(x) dx

This makes a lot more sense. Thank you for clarifying.

 

[mnmaa]

Re: 2012 HSC MX2 Marathon

fun question to do for anyone interested-
Suppose that f(1) = 2, f(4) = 5, f '(1) = 5, f '(4) = 4, and f '' is continuous. Find the value of the following integral.

the answer is 8

 

[Rezen]

Re: 2012 HSC MX2 Marathon

Prove that, for any triangle with sides a, b, c and area A,

a^2 + b^2 + c^2 >= 4sqrt(3)A

 

[Nooblet94]

Re: 2012 HSC MX2 Marathon

Here you go. I did it in as many steps as possible so you don't miss out on anything:

Wow, you were right about it being ugly.

 

[math man]

Re: 2012 HSC MX2 Marathon

Here you go. I did it in as many steps as possible so you don't miss out on anything:

oh poor carrot, so long lol.... Here is the shorter way: