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g(\frac {2x}{1+x^2}) =log\left ( \frac {1+\frac {2x}{1+x^2}}{1- \frac {2x}{1+x^2}} \right) = log (\frac {1+x^2+2x}{1+x^2-2x}) =log (\frac {1+x}{1-x})^2 \\ \\ = 2log(\frac {1+x}{1-x}) = 2g(x)

Whatever you do: MX1, Bio,Chem & Eco are solid disciplines; good choice. (I, for one, would like to be strong in the basic disciplines - they are the foundation for many different courses). Why not also do Physics as well and, of course an English of some sort. In the end, most people end up...

5:43 ?

$LHS $ = \frac {sin 2x}{cos 2x} \times \frac {cos x}{sin x} = \frac {2sinx\cdot cosx \cdot cos x}{cos 2x \times sin x} \\ \\ = \frac {2cos^2 x}{cos 2x} = \frac {cos 2x + 1}{cos 2x} = \frac {cos 2x}{cos 2x} + \frac {1}{cos 2x} = 1 + sec 2x

Some hate a subject because they are not interested in it. Some hate it because they cannot handle it (hopeless at it!). But if you need it, you need it.

In general, people in my generation have the view: if it requires Physics, then I'll just have to do it - whether or not I like it or are good at it. Make yourself better at it, if not necessarily very good at it. I cannot just do what I like; I must do what I need, even if I don't like it. You...

In some ways, I think, the new 4U will be easier. The Vectors part should be relatively easy.

If doing Optometry, maybe useful to do Physics (if current syllabus includes some Optics) as well.

For heaven's sake, don't drop to Standard to get high 90s. I'd rather a 70 in so-called Advanced than a 90 in Standard! You want as high a maths as you can manage: you never know what course you may want to pursue 4 years from now. What if it says it needs 5 or higher in 2U Advanced or even an...

I take this to mean: \int ^5 _4 vdt = \int _4 ^5 (4t + 5t^2) dt

Also some got in, but are intrinsically not up to scratch. They probably struggle during the last 2 or 3 years, as it dawns on them that they are not good enough to be in those schools. The reverse of this are students who fail to get into such top selective schools, for one reason or another...

If Data Science appeals to you, and requires a Masters, then make sure you first do your Bachelor's in an appropriate field. I myself have no idea what is required to become a Data Scientist. But compared to 40 or more years ago, today's Masters are not so difficult, as most are Course-based, if...

You can evaluate this as the sum of the sum of the 1st 20 terms of: a GP: 3 + 9 + 27 + . . . and of an AP: 1 + 3 + 5 + . . . \therefore \sum_{i=1} ^{20} = \frac {3(3^{20} - 1)}{3 - 1} + \frac {20}{2} (2 \times 1 + (20 - 1)\times 2)

\int ^{\frac{1}{3}} _0 \frac {e^{3x} }{e^{6x} + 1} dx =\int ^{\frac{1}{3}} _ 0 \frac {e^{3x}}{e^{6x} + 1} dx =\frac {1}{3} \int ^- _- \frac {1}{1 + (e^{3x})^2} d(e^{3x}) \\ \\ = \frac {1}{3} \left [ tan^{-1} e^{3x} \right ]^\frac{1}{3} _0 = \frac {1}{3}[tan^{-1} e^1 - tan ^{-1} e^0 ] = \frac...

I have not read the various posts above. But a newly emerging field for those who are strong in maths/statistics/IT? is Data Science (or whatever other names they may use) - people in such fields are very well paid. In my days what can you do if you majored in Maths? You can teach maths in...

y = sin(something) Since -1 <= x <= 1, the inverse cos can take the range of angles from 0 to 180 deg. So the sin can take all the values from 0 to 1. So range is: 0 <= y <= 1

Inverse Trig questions: a) easier to follow if you sketch a right-angled triangle, with acute angles A and B so that A + B = 90 deg. Let the sides be x, 1 (hypotenuse) and sqrt(1-x^2) so that sin A = x = cos B and sin B = cos A = sqrt(1-x^2) \therefore: sin^{-1} x = cos^{-1} \sqrt {1 - x^2} =...

one way: Prob (CAME) = (1/11)x(2/10)x(2/9)x(1/8) = 1/1980

To better understand: draw 2 associated right-angled triangles: 1) angle theta, with sides 2, root 5, 3 2) angle phi, with sides 3,4,5 cos \theta = \frac{2}{3} $ $ sin \theta = \frac {\sqrt 5}{3} \\ \\ tan \phi = \frac {3}{4} $ $ sin \phi = \frac {3}{5} $ $ cos \phi = \frac {4}{5} \\...

In a sense, the NSW HSC, unlike the IB, offers over 100 subjects to choose from. Students often choose the wimp subjects. In the IB, you must do Maths - but if offers 3 levels. Advice to drop maths, is unfortunate. If you keep maths, as you yourself have recognised, you have the option to do...