Mathematics Question Thread

[RuiAce]

I have a feeling that it should be less than 1.00 or less than 0.50. Because yeah, 0.00 is not possible mathematically.

Yet, if we're to be a bit technical here, we are using a continuous system to model a discrete system. It's physically impossible for there to be, say, 0.9 of an infected cell. Hence the actual answer is probably up to interpretation of the reader.

[katnisschung]

can you use the integration power rule for
definite integrals?

[jakesilove]

can you use the integration power rule for
definite integrals?

If you mean does



Then yes, it certainly does! You just then have to sub in your limits of integration

[katnisschung]

If you mean does



Then yes, it certainly does! You just then have to sub in your limits of integration

not quite this one...

tried using it for this question kept getting the wrong answer

find the volume of the solid of revolution that is formed when the curve
y=x^2+2 is rotated about the x-axis from x=0 to x=2

[anotherworld2b]

I am struggling to understand how small changes in differentiation works/how to use it.
Could i please have some help to understand it?

[Shadowxo]

not quite this one...

tried using it for this question kept getting the wrong answer

find the volume of the solid of revolution that is formed when the curve
y=x^2+2 is rotated about the x-axis from x=0 to x=2

that rule only works when it's x to the power of one, eg (7x + 4)⁵, x itself is only to the power of one but the whole bracket is to the power of 5 (or n)

[RuiAce]

I am struggling to understand how small changes in differentiation works/how to use it.
Could i please have some help to understand it?

Note to EVERYONE else - This is NOT in the HSC course. I have asked him to just post here for now.

[Shadowxo]

Well, dy/dx is the gradient, or the change in y divided by the change in x, or the change in y per x. f'(x) is the gradient at that particular point, or how much y is increasing with respect to x at that instant.
For 1:
Gradient = f'(x)=2x+4
f'(4) = 2*4+4 = 12
Gradient = f'(x) = change in y divided by change in x = ∆y/∆x = 12
∆x = 0.02
∆y = 12*∆x = 12*0.02 = 0.24 approximately
If you find f(4.02)-f(4) aka change in y, it's 0.2404, which is quite close

Edit: Rui beat me by 23 seconds but I'll post it anyway in the hopes it'll help

Hope this helps

[anotherworld2b]

Thank you for the help 
Could i also have help with this question please?

Edit: i have attached what i have tried to do

[anotherworld2b]

I have a quick question about the small changes question why did you input 4 into f'(x)?

[Shadowxo]

We input x=4 as we want to find the gradient when x=4
Think of it like finding and drawing the tangent, and using that to approximate the change in y

With your question, for Surface area I think you meant
SA = 2*L²+4*L*w
Doing this, I'd use L instead of w so you don't have to square root it

[anotherworld2b]

thank you for your help
For Q7 would you differentiate SA and make it equal 0? Then solve it to find x?
I am not sure where to go from there.

We input x=4 as we want to find the gradient when x=4
Think of it like finding and drawing the tangent, and using that to approximate the change in y

With your question, for Surface area I think you meant
SA = 2*L²+4*L*w
(I'll continue looking over for anything else)

[Shadowxo]

I've modified my post with my solution

[anotherworld2b]

ah I see
thank you very much for your help 
I was wondering would you have any tips on dealing with questions on the application of differentiation? We were just taught this so I am still relatively a newbie that is slow to understand what to do.

We input x=4 as we want to find the gradient when x=4
Think of it like finding and drawing the tangent, and using that to approximate the change in y

With your question, for Surface area I think you meant
SA = 2*L²+4*L*w
Doing this, I'd use L instead of w so you don't have to square root it

[RuiAce]

We input x=4 as we want to find the gradient when x=4
Think of it like finding and drawing the tangent, and using that to approximate the change in y

With your question, for Surface area I think you meant
SA = 2*L²+4*L*w
Doing this, I'd use L instead of w so you don't have to square root it

Pretty sure this solution is correct. I'm just pointing out a technicality problem.

Not too fussed about it, but when differentiating, preferably use the parentheses: \(\frac{d(SA)}{dL}\). Otherwise, it causes confusion with this nonsense: \( \frac{dS}{dL}\times A\)