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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread What do you mean? We can't mention the 'tangent' in our definition of 'tangent', since that'd be a bit of a circular definition.

Re: HSC 2016 3U Marathon Lol, realised it just as I was waiting for this page to load.

Re: HSC 2016 3U Marathon What is S2P and P2S?

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I know. It's just then we shouldn't say it's the value of the derivative there, since the derivative would technically be undefined there.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent To do the question you were asking about, recall that we found the equation of the tangent to the curve at $x=a$ earlier. Using this equation, the point $(c,0)$ lies on a tangent if and only if there exists $a$ in the...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread A tangent line doesn't need to only touch the curve once. It needs to share the same point at some point on the curve, and also match the slope there, where the slope is the value of the derivative there (assuming the slope isn't...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread What is the question?

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent For the first one, $xy = u$. Then differentiate both sides with respect to $x$ (use the product rule for the L.H.S.).$ $\noindent For the second one, $uy=x$. Then differentiate both sides with respect to $x$ (use...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread For part (a), you can use parametric differentiation. For part (b), do it as they say to do it.

Re: MX2 2016 Integration Marathon $\noindent This answer ($4\pi$) would be the case if the integrand were $1$, but it is $x^2$ in fact. The triple integral $I$ can be set up as the following iterated integral: $I=\int _{y=-2} ^{y=2} \int _{x=-\frac{1}{2} \sqrt{4-y^2}} ^{x=\frac{1}{2}...

There was a Sydney Morning Herald article about that paper: http://www.abc.net.au/news/2013-11-06/hsc-maths-paper-too-hard-claim-teachers/5074070

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Yeah, it can be pretty useful for doing tedious derivatives of long products :). But it's rare that they'd make you do a differentiation involving a product of three (or more) functions in the HSC I think.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread If you don't know logarithmic differentiation, you can read about it on this old thread: http://community.boredofstudies.org/14/mathematics-extension-2/79552/interesting-possible-trick.html . (Or search it up online.)

Maybe you just made a silly algebra error or something, so you might want to post your working so far. :)

These are the same type of question. Integrate the given rate of change to get the required function + C, then sub. in the given conditions to solve for C.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Maybe post your working, since it could just be a silly mistake.

They probably wouldn't mind in MX2 if you just assumed it was monotonically increasing, unless that Q. was worth a lot of marks.

If we ignore all external forces though (so ignore gravity), there is this result: https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation .

I think I did something similar here for constant gravity: http://community.boredofstudies.org/18/physics/344618/hsc-physics-marathon-2016-a-4.html#post7069436 $\noindent For varying gravity, the differential equation is harder to solve if I recall correctly (I think I thought about this before...

$\noindent The pyramid $\mathcal{P}$ has volume $V_{1}=nV = \frac{r^2 h}{6} n\sin \frac{2\pi}{n}$. Since the volume of the cone is $V_2 = \frac{\pi r^2 h}{3}$, we have the ratio of the volumes $\rho $ being $\rho \equiv \rho_n :=\frac{V_1}{V_2}= \frac{\frac{r^2 h}{6} n\sin...