VCE Methods Question Thread!

[kinslayer]

how do you do this question? im not sure how to implement the 100cm^3 sand. Answers B

volume of prism V = Ah

dV/dt = 4 cm^3/min

dV/dh = A, dh/dV = 1/(A cm^2)

dh/dt = dV/dt * dh/dV = 4/A cm/min

The current volume of sand in the prism is irrelevant, unless that volume is greater than V = Ah in which case the prism is full and dh/dt = 0 aheh

[maddihanna]

Is there any chance someone could help me out with this calculus question?
Thank you!

[cosine]

Is there any chance someone could help me out with this calculus question?
Thank you!

Break it down to pieces:

1). Always observe when/where the gradient is equal to zero, that is, where do we have a stationary point?
Those three dots all have zero gradients, so on the gradient function graph, those exact x values will be x-intercepts. Now call the one to the left A, the one at x=0 B, and the one on the right C.

2). Gradient positive or negative?
Now Look at the gradient of the left of A, is the gradient positive or negative? (Look at the shape of the slope). Everything to the left of A has a negative gradient, also everything between point A and B is negative. Note that x=A and x=B are not a negative gradient, because as we afore mentioned, they are stationary points. This means f'(x)<0 = {x: x<A} u {x: B>x>A}

Ill leave the rest to you, hopefully you can do the same thing I did, i hope this helps!

[garytheasian]

Is the answer to c) 7 just want to make sure since there are no solutions availiable.

[kinslayer]

Nice filename on the image.

we want to solve

[garytheasian]

Nice filename on the image.

we want to solve

Thanks man appreciate it

[knightrider]

For this question .

Wouldnt the answer to this be undefined as there is a vertical asymptote at x=0.

But the book has the answer .

Who is right and why?

[kinslayer]

For this question .

Wouldnt the answer to this be undefined as there is a vertical asymptote at x=0.

But the book has the answer .

Who is right and why?

Integrand isn't defined at x = 0, so this is an "improper" integral. The integral should be



The integral is equal to ln(2) - ln(t). As t approaches zero from the right, -ln(t) approaches infinity, hence the book's answer.

Also, are improper integrals a part of Methods now? wot

[knightrider]

Integrand isn't defined at x = 0, so this is an "improper" integral. The integral should be



The integral is equal to ln(2) - ln(t). As t approaches zero from the right, -ln(t) approaches infinity, hence the book's answer.

Also, are improper integrals a part of Methods now? wot

Thanks kinslayer   

so if i wrote the integral is undefined as my answer due to the asymptote at x=0.

Would i be wrong?

[biy]

Guys my class has started probability, and I really suck at it. Like literally suck at it..

How can I improve this?

[IndefatigableLover]

Guys my class has started probability, and I really suck at it. Like literally suck at it..

How can I improve this?

Best way to go about it is to just do the textbook questions (preferably Essentials including Chapter Review for Probability if you can) and soon enough you'll pick up on the "wording" (which is what makes it hard initially but once you expose yourself to the types of questions they ask, it's relatively straight forward from there since there's only 'this' much they can ask you in comparison to say Calculus).

[cameotodd]

Hi can someone help me with these two questions? (see attached)

Thank you

[garytheasian]

b is hard

[RazzMeTazz]

For the worked example question from my textbook (attached below) I don't really understand why the derivative of the function is 2x-4 if x^2-4x >0 and is -2x+4 if x^2-4x < 0.

I don't really understand how the x^2-4x part comes into being part of the domain of the derivative?

Any help would be appreciated!

[Floatzel98]

b is hard

Well just differentiate A with respect to r and you get . Make it equal to 0 and then just 'solve' for one of the variables.

So





For ii), i'm pretty sure you get something theta in terms of L to show the area from a), so i would just sub it into there.

For iii), a stationary point occurs at r = L/4, so then you can show the nature of that point. But i'm not exactly sure how to determine what kind of stationary point. Maybe you could say that because the equation for Area takes the form of a parabola and the x^2 term has a negative coefficient, the point is a max?

soz i'm not kinslayer