Mathematics Question Thread

[owidjaja]

Hey guys,
I'm a bit unsure how to do question d).

Thanks in advance

[Opengangs]

Hey guys,
I'm a bit unsure how to do question d).

Thanks in advance

Note that \( x = 2 - t - t^2 \) can be factored nicely to give: \( x(t) = (t + 2)(1 - t) \).
What's neat about this is that we can graph this and see what's happening around the interval \( [0, 2] \), which is what we're interested in.



Now, we notice that the particle starts at \( t = 0 \) and finishes at \( t = 2 \). So it must travel first from \( t = 0 \) to \( t = 1 \), and then \( t = 1 \) to \( t = 2 \).

Now, between \( t = 0 \) and \( t = 1 \), we see that it would have travelled \( x(0) = 2 \) units because it would have taken the particle 2 units downwards to get to \( x = 0 \). Now, it will continue to travel downwards until it hits \( x(2) = -4 \). Thus, it travelled 4 units (just in the downwards direction). So if we consider the path the particle takes between \( [0, 2] \), we see that it 2 + 4 = 6 units altogether.

Whenever you're not sure where to start, I recommend visualising it or draw a diagram to aid with your working.

[Yiruma]

Hey guys, I have a question for 2 unit maths integration!

find the exact area bounded by the curves y=sin x and y=cos x in the domain 0<x<2pi

[Opengangs]

Hey guys, I have a question for 2 unit maths integration!

find the exact area bounded by the curves y=sin x and y=cos x in the domain 0<x<2pi

Hey, Yiruma!

Have you drawn a diagram? If not, that would be a good place to start.
Let me know if you have any problems

[jamonwindeyer]

To secretweapon/GMT/Lear, I've split your chat off this thread and moved it to the Methods section

Click here!

[kauac]

When asked to differentiate using first principles, which formula should I use?

My textbook works through three different formulas for the same example...So, I was wondering whether it just preference, or if some formulas suit particular questions more than others??

[RuiAce]

When asked to differentiate using first principles, which formula should I use?

My textbook works through three different formulas for the same example...So, I was wondering whether it just preference, or if some formulas suit particular questions more than others??

Ignore the extra stuff maths in focus puts there for no good reason and just use \( \lim_{h\to 0}\frac{f(x+h)-f(x)}{h} \)

(Remark: The formula \( \lim_{x\to c} \frac{f(x)-f(c)}{x-c} \) is good for mathematicians to establish where differentiation comes from in the first place. But to actually use it is a waste - it overcomplicates calculations.)

[terassy]

Am I correct? When using the Simpson's rule, one application uses three function values and two applications uses 5 function values. And when using the  Trapezoidal rule, one application uses two function values, and two applications uses three function values and so on.

[jamonwindeyer]

Am I correct? When using the Simpson's rule, one application uses three function values and two applications uses 5 function values. And when using the  Trapezoidal rule, one application uses two function values, and two applications uses three function values and so on.

You are indeed correct

[LaraC]

Hello

Just trying to do a bit of revision and I got a little stuck on this question. I have the first derivative and a point it passes through and I have to find the equation of the curve.

dy/dx = 6x^2 + 12x -5
If the curve passes through the point (2,-3), find the equation of the curve.

Thanks in advance!

[Opengangs]

Hello

Just trying to do a bit of revision and I got a little stuck on this question. I have the first derivative and a point it passes through and I have to find the equation of the curve.

dy/dx = 6x^2 + 12x -5
If the curve passes through the point (2,-3), find the equation of the curve.

Thanks in advance!

Hey, LaraC.

So what you'd want to do is to integrate it to find the equation if the curve (don't forget your constant of integration).

And using the fact that it passes through (2, -3), are you able to finish it off?

Let me know if you have any problems.

[LaraC]

I have another question sorry guys!! 
A rectangular prism with a square base is to have a surface area of 250cm^2. Its volume is given by V=(125x - x^3) / 2
Find the dimensions that will give the maximum volume.

I started by differentiating the volume formula....is this the right way to go or not? I can't remember sorry!!

Thankks!!

[RuiAce]

I have another question sorry guys!! 
A rectangular prism with a square base is to have a surface area of 250cm^2. Its volume is given by V=(125x - x^3) / 2
Find the dimensions that will give the maximum volume.

I started by differentiating the volume formula....is this the right way to go or not? I can't remember sorry!!

Thankks!!

Yeah.

Now set \( \frac{dV}{dx}=0 \) to find the value of \(x\) that maximises the volume. And remember to test that it is a max, as with all problems of this nature.

[LaraC]

Thanks a million RuiAce!! #manyrespectpoints!!
So in this case it is a cube with dimensions 6.4cm x 6.4cm x 6.4cm....
But what about in the case it wasn't a cube, and had three different dimensions? Would there be three different stationery points and the three dimensions would be those three x values?

Sorry I don't have any specific question here, I'm just wondering in general as this type of question seems to crop up a bit 

[RuiAce]

Thanks a million RuiAce!! #manyrespectpoints!!
So in this case it is a cube with dimensions 6.4cm x 6.4cm x 6.4cm....
But what about in the case it wasn't a cube, and had three different dimensions? Would there be three different stationery points and the three dimensions would be those three x values?

Sorry I don't have any specific question here, I'm just wondering in general as this type of question seems to crop up a bit 

From what I've seen when there's multiple stationary points in 2U, most of the time the other ones are all for negative values of \(x\). Which we can typically discard for various reasons (e.g. side length cannot be negative).

But that's exactly why we must test for a max/min. Usually if both stationary points end up being at positive values of \(x\), one of them gives a min whilst the other gives a max.

(The techniques for 3+ stationary points are more advanced and require more work, but I've never seen that appear in 2U as of yet)