4U Maths Question Thread

[clovvy]

Did you get this question off the meme? (It's final answer is actually quite disgusting.)

I did check the answer and it is disgusting, how do you guess that? (I mean you are right)- how do I approach this whole mess to get to the final answer?

Is this question beyond 4U?

[RuiAce]

I think, once you're at that point, you might wanna try bashing it with a trig substitution. (Sadly hyperbolic substitutions are not taught in 4U)

In my opinion, it's a waste of time and you can be doing something way more productive than that. However if you have enough time to do it, make sure you include the boundaries and check with WolframAlpha as you go.

[RuiAce]

Managed to finish it off but yeah I used a hyperbolic substitution, which is beyond 4U. The thought of subbing in \( u = \sec \theta\) horrified me.

But yeah, this is still a brute forced approach. I haven't been able to see anything elegant to bash this one with.

[tiffany88]

Hello,
Could I please get some help with part b of this question?

[RuiAce]

Hello,
Could I please get some help with part b of this question?

The concept of Riemann sums are not involved in the MX2 course. Where is this question coming from?

[tiffany88]

The concept of Riemann sums are not involved in the MX2 course. Where is this question coming from?

I got it from my tutor, who did these questions involving Riemann sums for integration. I'm glad its not part of the course because it seems difficult to understand

[RuiAce]

It's covered in first year uni because Riemann sums form the basis of the integration that we do (which is, incidentally enough, known as Riemann integration). The most that you'd be required to do with rectangles in 4U is use them to prove inequalities that involve integrals. The whole ideas of generalising this (replacing one rectangle with multiple rectangles, taking limits etc.) however is not important so I won't cover it here.

(However, if you want a solution anyway, you can find the first year uni math questions thread, repost it there and I'll be happy to address it.)

[RustyWasTaken]

Help please :p
Cheers

[RuiAce]

Help please :p
Cheers

[clovvy]

https://www.youtube.com/watch?v=F9ZJya5DK5w
Another way of approaching the meme integral

[clovvy]

[RuiAce]

\begin{align*}\int \frac{dx}{x+\sqrt{x}}&= \int \frac{dx}{\sqrt{x} \left(\sqrt{x}+1\right)}\\ &= 2\int \frac{du}{u+1}\\ &= 2\ln |u+1| + C\\ &= 2\ln \left( \sqrt{x} + 1\right) + C\end{align*}

[vikasarkalgud]

Error

[RuiAce]

Hey Rui, this is a different kind of problem but I don't know where else to ask, I'm doing a software major and have encountered a math problem. Using C# on Visual Studio, and for some reason, the square root is coming as square root of -23. It seems to be doing 4 - (3 * 9), instead of 3 * 9/169 which is 27/169 (what I'm meant to get since 3 - that, would give me a value I can square root.

With inputs:
a = 8
b = 5

Formula:

perimeter = (Math.PI) * (a + b) * (((1 + (3 * ((a - b) * (a - b) / (a + b) * (a + b)) / (10 + Math.Sqrt(4 - (3 * ((a - b) * (a - b) / (a + b) * (a + b)))))))));

the square root im dealing with is on 2nd half of that mess
I know, brackets at end are crazy but there seems to be that many since no syntactical error. During runtime, I placed a breakpoint and perimeter value returned 'NaN', or '0' when variable was hovered over. what is wrong? Also, you've probably realised that there is an approximation for the perimeter of the ellipse, assuming ive copied it right...

Any help would be much appreciated, ty

Fairly sure programming languages aren't in the HSC altogether, so if this is something more related to uni stuff then please make a new thread in the uni section of the forum.

Also, it's really not good practice at all to nest so many brackets. If you really wanna do that you should declare some new variables "e.g. sum = a + b and diff = a - b" instead. And maybe doing some divisions step by step. Because looking at that, I really can't tell what's going on

[clovvy]

Hey guys,
how do I recognise horizontal or vertical tangents at a stat point or an asymptote, thanks