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For h), the first and last forms are fixed. The remaining eight can be either yes or no, but exactly four (any four) must be yes. So choose four from eight: ^8C_4=\binom{8}{4} = 70.

Honestly, that question was more annoying than all of Q16 put together.

\int_\pi^{3\pi/2} \frac{\sin x}{\sqrt{1+\sin 2x}}\,dx = -\frac \pi 4

\int_{3/8}^{5/12} \frac{\pi(4x^2+1)-2}{(2x\sin \pi x+\cos \pi x)^2}\,dx = \int_{3/8}^{5/12} \frac{\pi(4x^2+1)-2}{\left(\pm \sqrt{4x^2+1} \sin (\pi x + \arctan(1/2x))\right)^2}\,dx \qquad \text{(auxiliary angle method)} = \int_{3/8}^{5/12} \left(\pi - \frac{2}{4x^2 + 1}\right)\csc^2\left(\pi...

The point is that someone who posted here 16 years ago probably isn't around to give you an answer.

======================================================== Session Course Title Result ======================================================== T2 COMP1521 Computer Systems Fundamentals....91 HD T2 MATH1241 Higher Mathematics 1B............91 HD T2...

What argument is this?

Visual Basic, but we were free to use any language we wanted (e.g. C#, JS) for assignments and such.

This is fine, no? \begin{aligned} g &= f^{-1} \\ f(g(x)) &= x \\ f'(g(x)) \cdot g'(x) &= 1 \quad\text{(differentiate w.r.t. }x) \\ \implies g'(x) &= \frac{1}{f'(g(x))} ,\end{aligned} as f'(g(x)) \neq 0.

It depends on what exactly is meant by "continuous". When we say a function is continuous we usually mean either of two things: 1. the function is continuous at every point in its domain. In this sense, functions like \tan are considered continuous, and so is f . Because \pi/2 is not in...

What are the other differences between this and the fx-82? Is it just being able to do arithmetic with complex numbers and the normal distributions thing?

Yep. That's the problem when you prescribe and assess the same texts year after year. If you truly want to, you'll be able to find a way.

Although I really hated HSC English (because it compulsorily counted towards the ATAR and most of it was not useful), I found the analysis skills involved to be occasionally useful - for example, when you're watching a movie or playing a story-driven game. You're never expected to be able to do...

Admittedly, I went through a lengthy process (including looking up a standard integral table for \text{sech} ) and it was only at the end I realised that everything I did could be compressed into one substitution.

4. \int_0^\infty \frac{x^2}{x^6+1}\,dx = \frac 13 \int_{0}^\infty \frac{1}{u^2+1}\,du \quad (u = x^3) = \frac 13 \cdot \frac \pi 2 = \frac \pi 6.

I have a feeling this is not the fastest method... I = \int_0^1\left( \arcsin\left(\frac{x}{x+1}\right)\right)^2\,dx =\int_0^{\pi/6} \frac{y^2\cos y}{(1-\sin y)^2}\,dy \quad \left(y = \arcsin \left(\frac{x}{x+1}\right) \iff x = \frac{\sin y}{1-\sin y }\right) =\frac{\pi^2}{18}- 2...

For UNSW there is a difference between Adv Sci (Mathematics) and Adv Math, at least in terms of program structure. For example, MATH1081 is compulsory for Adv Math but not Adv Sci. The 2nd/3rd year core courses for Adv Sci and the Adv Math streams are also different. For the normal Science...

It's whichever one you're personally interested in more. Scaling is nice, but if you don't enjoy the subject then you'll need to put in a lot of effort to get a good mark.

If one of them is clearly more convenient, then pick that one. For example, if we have the system \begin{cases} 2x+7y &= 4 \\ 4x + 15y &= 3\end{cases} Then it would be smarter to eliminate x by doubling the first equation. The alternative is to multiply equation 1 by 15 and equation 2 by...

A system of simultaneous equations is just a set of conditions. When we solve a system like this, we're simply finding and using different equations that represent the same conditions. Point being, whether you choose to do this step or that step first doesn't matter, because nothing you're...