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so were you the first time you saw it

du=-\sin x\ \!dx \therefore\textstyle\int\sin^3x\ \!dx=\int-\sin^2x(-\sin x\ \!dx)=\int(\cos^2x-1)(-\sin x\ \!dx) \textstyle=\int(u^2-1)\ \!du=\frac{u^3}{3}-u+c=\frac{\cos^3x}{3}-\cos x+c

If you only include real numbers, as f(x) approaches \infty, then 1/f(x) approaches 0 but does not reach it, hence the open circle at (4,0).

Obviously the competent maths teacher would teach you the beta and gamma function methods, as that gives much quicker solutions.

Here is a quicker way using beta and gamma functions \textstyle I_{2n}=\frac{1}{2}B(n+\frac{1}{2},\frac{1}{2})=\frac{1}{2}B(n-\frac{1}{2},\frac{1}{2})\cdot\frac{n-\frac{1}{2}}{n-\frac{1}{2}+\frac{1}{2}}=\frac{2n-1}{2n}I_{2n-2} \textstyle...

here is one way

like this?

like this?

Opernhaus Zürich did a new version of Der Ring des Nibelungen conducted by Gianandrea Noseda. Das Rheingold is at https://player.vimeo.com/video/948460812?h=ddc34ee508 Die Walküre is at https://player.vimeo.com/video/948650345?h=33320f3143 Siegfried is at...

One of the authors of Maths in Focus textbooks has responded with the following: Students who take an easier level of maths for the HSC because the harder levels don't raise their ATAR may find that it comes back to bite them at university. They will be less prepared for science-based courses...

Chairman of uac scaling committee and director of academic profiles disagree about atars. http://4unitmaths.com/hard-maths-for-hsc-doesn't-add-up.pdf If you get high atar with easy courses, get into uni doing maths-related degree which had prerequisites removed, do you think you will survive...

The graph has been tidied up and turned into a tikz picture so this version looks better

This is a bit shorter

Here's a bit of maths trivia. Do you recognise this guy from the ABC? Tony Jones. Well the Jones in the Jones and Couchman 3 unit books was his father! (Stanley Bruce Jones)

There are other old ebooks available too, but some came out in the 1990's Fitzpatrick 3u and 4u (old syllabus) Arnold and Arnold 4u Patel Old editions of Terry Lee Jones and Couchman 3 unit like this:

So these are available as ebooks: these are not as far as I can tell: nor are the Lush and Smith, nor Mulhall and Smith-White, again as far as I can tell.

Some are listed at http://4unitmaths.com/texts.pdf Coroneos and Lynch, Mulhall and Smith-White as well as the Lush and Smith books for Level 1 These were superseded by Coroneos’s watered down 4 unit book in 1981 and his 4 unit supplement 3 unit was originally called Level 2F. Coroneos and...

y 11 cambridge ext 1 16B Q8 (also y12 cambridge advanced 7F Q16)