VCE Specialist 3/4 Question Thread!

[BlinkieBill]

Hey,
is is this type of question still in the study design??
eg. Find the integral of 1\(x^2 + 1)^2 using the substitution x=tan u

thq

[Syndicate]

Hey,
is is this type of question still in the study design??
eg. Find the integral of 1\(x^2 + 1)^2 using the substitution x=tan u

thq

Yep

[Gogo14]

Why is the area the derivative of the volume? This has been explained before, but I still dont intuitively understand why

[zsteve]

Why is the area the derivative of the volume? This has been explained before, but I still dont intuitively understand why

Hey! Here's a quick-and-dirty way of understanding it...
We can define a infinitesimal volume dV as . If we rearrange this, we obtain . (this is using differentials, which is kind of dodgy in VCE Spesh but nonetheless works).

[Gogo14]

How would you integrate this using u substitution by hand? Thnx

[Sine]

This is linear substitution so a little different from usually substitution

From this we also can say that







now let's sub back in the x's

[deStudent]

http://m.imgur.com/SgAvlZd

Will VCAA accept if we write the answer for part a and b like this:
a) y= e^(1/2x^2 +c)
b) y= e^(1/12x^3 +c)

Thanks

[Sine]

http://m.imgur.com/SgAvlZd

Will VCAA accept if we write the answer for part a and b like this:
a) y= e^(1/2x^2 +c)
b) y= e^(1/12x^3 +c)

Thanks

Yup it's fine - and most exams will give you initial conditions to allow you to solve for c
You could also do something like this



Where A = e^c (though I always thought this was a bit over the top)

[deStudent]

Yup it's fine - and most exams will give you initial conditions to allow you to solve for c
You could also do something like this



Where A = e^c (though I always thought this was a bit over the top)

Thanks.

Also when they give you that initial condition, sometimes the differential equation will cause you to take the square root or have 'y' inside the natural log. This means when solving for 'y' you'll need to determine if y is positive or negative square root/modulus if you choose to make y the subject. Is this necessary to solve for y or would leaving the differential equation as "y^2=..." or ln|y|=... be okay?

[Sine]

Thanks.

Also when they give you that initial condition, sometimes the differential equation will cause you to take the square root or have 'y' inside the natural log. This means when solving for 'y' you'll need to determine if y is positive or negative square root/modulus if you choose to make y the subject. Is this necessary to solve for y or would leaving the differential equation as "y^2=..." or ln|y|=... be okay?

Usually y will have a restriction such that you will be able to determine what you can and can't assume.

[Shadowxo]

Also Sine mentioned before sometimes they make it into Ae^1/2x2 for example - this is often so they can get rid of the modulus sign, as A is ħe^c
So if you had |y|=e^1/2x2+c you could make it into y=Ae^1/2x2, and solve for A without having to worry about whether it's positive or negative (finding A will determine that)

[joejoh]

Does anyone know how to sketch subsets of the complex plane (e.g. circles, rays etc.) using a CAS? If anyone knows please let me know.
Cheers,
Jo

[deStudent]

http://m.imgur.com/a/59FOR

For part b) I understand the working on the image of the solution but I don't understand why you have to do it like that? Isn't the volume constant, so wouldn't the rate out = x/400 * 1. Therefore dy/dx = 2/5 - x/400? So V = 400, not 400 + t?

Thanks

[Shadowxo]

http://m.imgur.com/a/59FOR

For part b) I understand the working on the image of the solution but I don't understand why you have to do it like that? Isn't the volume constant, so wouldn't the rate out = x/400 * 1. Therefore dy/dx = 2/5 - x/400? So V = 400, not 400 + t?

Thanks

For part b, the flow in is 2 L/min and flow out is 1 L/min. As these are not the same, the volume changes as the amount of water going in is more than the amount going out, so the volume will increase, that's why you can't use a constant volume.

[deStudent]

^^^Thanks.

For the Ti Nspire is the easiest way to solve Euler Method type questions with the spreadsheets screen?