Recent content by tywebb

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

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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