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$\noindent The range of the piecewise function will be the union of the two ranges posted by kawaiipotato above (the second of which should be written $(-\infty, 1)$ of course.). So the range is $(-\infty,\infty)$, or in other words, $\mathbb{R}$.$

It depends what you mean by "matter". It's not like there's a theoretical "ATAR cap" based on your school rank or anything if that's what you were thinking.

Re: Several Variable Calculus The basic ideas are: - When x = 0 or 1 (the endpoints of the domain), f_n (x) = 0 for every n, so the convergence at these x is clear. - For any given x in (0, 1) (interior of the domain), the fact that exponential decay dominates power function growth yields...

Yes. It is even theoretically possible to get 99.95 ATAR with English Standard.

$\noindent Yes, but they don't know how to integrate $\sin^{-1} x$ in 3U. So they would be expected to use other methods.$

$\noindent Try sketching the graph of the cubic $y = (x-a)^2 (x+b)$ and deducing the solution to the inequation from that. If you're not sure how to sketch that graph, you should learn this first.$

Because the graph was of y = f(x). The solution will be the set of x values for which the curve is below the x-axis.

Sketch the graph.

If you want the actual physical area, it's the one using absolute values. The thing that is 0 is the signed area, or net area. If we just say "area" of a function on an interval without saying "signed area" or "net area", we would probably be referring to the physical area, which is always...

Re: MATH2601 Linear Algebra/Group Theory Questions No it need not be. Say V = R^2 and W1 = R^2 (= V) and W2 be the line (t, 0) (the x-axis). Take T to be a rotation map by 90 degrees counter-clockwise about the origin say. Then T is a linear map from V to V, so T(V) = T(W1) is a subspace of W1...

"Dropkick" relative to the average at those schools maybe.

Yes, the inverse's domain will be the range of the original function.

In fact, the median ATAR at James Ruse last year was 99.2 (mentioned near the bottom of this page: http://www.jamesruse.nsw.edu.au/about/achievements (as at 22 May, 2017)).

The slope m is 3, not 1/3.

$\noindent Use the fact that if a line with slope $m$ makes angle $\theta$ to the positive $x$-axis, then $\tan \theta = m$.$

Re: MATH1131 help thread No, that point doesn't affect whether the line will be parallel to the plane.

Re: MATH1131 help thread That is correct.

Did this post by Mahan1 make sense to you?: http://community.boredofstudies.org/12/mathematics/361960/maths-help-please.html#post7240008 .

No (assuming you draw it yourself, without using a computer to do it or something).

Use your knowledge of basic functions. Alternatively, note that the graph is the lower-half of a certain circle.