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Not quite, for example, the function y=x^4 has y''(0)=0, but 0 is NOT a point of inflexion of y=x^4, as y=x^4 just looks like a parabola. The key is that concavity must CHANGE on either side of a point of inflexion. Ie, we are looking for maxima and minima of y' rather than just looking for...

Re: HSC 2013 4U Marathon "\," is a common spacing string used to separate integrand from the "dx".

Re: Chess thread? I'll be up for a game later as well.

Re: Chess thread? yep just tuning in now.

Re: Chess thread? Part of the point of double elimination tournaments is that it takes two losses to knock you out.

Re: Chess thread? Now that uni and school will be dying down for people, we should get regular games in. How would people feel about a tournament with say weekly or biweekly rounds? Watching the world championship has made me hungry for match play, so we could do something like a double...

No, the remainder is the thing you neglect. The point of long division is you can write: p(x)/q(x) = f(x) + r(x)/q(x) where r is your remainder and deg(r) < deg(q). Since q has higher degree than r, the ratio r/q tends to zero for large x, so p/q has an oblique asymptote f.

Long division is the best way really.

d/dx has no meaning then. it is like having a square root sign with nothing inside it.

d/dx is notation for the operation of differentiating w.r.t x. dy/dx is what you get if you apply this operator to a specific function y(x). ie "Find d/dx(blah)" means differentiate blah with respect to x.

make solid eye contact and don't stop.

Haha I thought so, just can never be entirely sure on the internet.

Huh?

How was I trolling? My explanation was beyond syllabus because the motion of a large amplitude pendulum is beyond syllabus. A properly designed pendulum would not "bobble around" markedly if we increase angle size, and there is neglible difference in the experimental error between an angle of...

Also, if the pendulum has enough initial momentum that it's angle will at some stage exceed pi/2 then the analysis is even more complicated.

Nothing, it still moves from side to side, but simple harmonic motion is no longer an accurate description, and we have no easy way of calculating period in terms of g.

Uhh no, the string will always "experience tension". If gravity was the only force acting, then the weight at the end of the string would fall straight down, not swing. The reason we keep the angle small is that when we solve the differential equation for the motion of a pendulum in terms of...

I use programs like inkscape to create diagrams (or even better something like kig for geometric figures) and then import them into my tex files. Ends up looking pretty good.

Let me know when, I am guessing my schedule is probably more flexible than yours atm.

And to be more specific, one of the most marked examples of beauty in mathematics is the prime numbers. Here you have objects which you could define to an intelligent primary school kid, and yet there are questions about them that have been asked for THOUSANDS of years but not answered. (For...