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No logical reason.

\sin \left (3x \right )\leq 1\;\; \forall x\in \mathbb{R} but yes.

I did not find the volume of the cylender as the explicit answer; would you agree that: The volume when the region bounded by the curve y=x^3, x=2 and the x-axis (x>0) is rotated about the x-axis PLUS The volume when the region bounded by the curve y= x^3, the y axis and the line y=8...

Required\;volume\; =\pi \times 8^{2}\times 2-\pi \int_{0}^{2}\left (y \right )^{2}dx =128\pi -\pi \int_{0}^{2}\left (x^{3} \right )^{2}dx =128\pi -\pi \int_{0}^{2}x^{6}dx =128\pi -\frac{\pi}{7}\left [x^{7} \right ]_{0}^{2} =128\pi -\frac{\pi}{7}\left ( 2^{7}-0^{7} \right ) =128\pi...

Just checked on a spreadsheet, took n as 10, 100 and 1000 and did the summation, and yes what you have stated seems to be correct.

Over what range of n are you talking about, because it is NOT true for n=2: 2!=2\times 1\times 0!=2< \left ( \frac{2+1}{2} \right ) ^2=\left ( \frac{3}{2} \right ) ^2=2.25 \ EDIT: A quick look at this using a spreadsheet reveals that the converse of what you stated is true for all natural...

:wave:

\mathbf{i}=\begin{pmatrix} 1\\ 0\\ 0 \end{pmatrix} , \mathbf{j}=\begin{pmatrix} 0\\ 1\\ 0 \end{pmatrix} , \mathbf{k}=\begin{pmatrix} 0\\ 0\\ 1 \end{pmatrix} , \mathbf{i},\mathbf{j},\mathbf{k}\in \mathbb{R}^{3} Using column vectors.

Q1 of MC. 2008 Independent Trial. The answer is definitely (c), although i understand where you get the idea it could be (b). Since the instructions state to "Select the alternative A, B C or D that bet answers the question", (c) is the best answer. Choosing (b) implies a substitution...

Which year's Independent trial examination are you referring to?

Re: outline the essential problem with light, the aether and the principle of relativ He definitely was the first to formally state it, but i read somewhere that that the ideas behind it does pre-date him.

Past semesters' unit outlines have been placed here: ECON241: Introductory Econometrics - Department of Economics - Macquarie University and it should be updated with 2010, semester 1 in the not-too-distant future hopefully.

It is possible with a (variety of) good textbooks.

The textbook [in my opinion] is not needed because the lecture notes are excellent, and extra questions and more detailed lecture notes are available for all topics. I don't think you will have time to go through the textbook if you go through the rest of the material. That's for techniques...

It appears ECON111 has changed quite significantly, so i don't think we can help you. Last year a different textbook was used, tutorials did not start unitl week 4 (yes, four, no typo), and 'tutorials' were held in lecture theatres with 100+ students registered for (but not necessarily 'went...

For all fee information, refer to University Fees, Macquarie University.

Yes, whether it be an upfront payment or not; i.e. any payment received after 19 February, 2010.

There is no pack since ECON111 no longer uses Bernanke.

The box you ticked on the eCaf form is only an indication; that is, if you don't pay even though you ticked you would, and you have HECS HELP approved, your outstanding debt will be transferred to the ATO 2 weeks after census date (31 March) as normal.

ACST101- - Starts in week 2.