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Your answer would be n*pi/2 rather than n*pi, as you can see by splitting up into cases of n even (n = 2k), or n odd (n = 2k-1).

$\noindent For your particular question, our function being integrated is $f(x) = x^{j}$, where $j$ is a fixed positive integer. Our interval of integration is $[1,2]$. The partition is given to us as $\mathcal{P} = \left \{1,q,\ldots ,q^{n}=2\right \}$, where $q = \sqrt [n]{2}$. The $i$th...

We would go to the general formula. The nth partial Riemann sum formula is: $$S = \sum_{i= 1}^{n} f\left(x_i ^{*}\right) \Delta x_i$$, where $\noindent we have partitioned the interval as $\mathcal{P} = \left \{a = x_0, x_1, \ldots , x_{n-1},x_n = b\right \}$, $x_i^{*}$ is some point in our...

sin(3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x). Now, use double angle formulas (for the cos(2x), use 1 – 2sin2 x), and use Pythagorean identity when necessary.

To derive that triple angle formula, you can apply the compound angle formula to sin(2x + x).

An alternate method to leehuan's is to derive and use a sums-to-product identity.

Yeah Black-Scholes and its relation to the heat equation was one thing I had in mind. "It [heat equation] also can be used to model some phenomena arising in finance, like the Black–Scholes or the Ornstein-Uhlenbeck processes." (From...

Actually (incidentally) a lot of the models in Finance have come from Physics (or have connections to mathematical models used in Physics).

As in the HSC subjects aren't listed as compulsory/prerequisite, just 'assumed knowledge', so even if you haven't done them in the HSC, you can enrol in degrees that have them as assumed knowledge.

Maybe they've realised their mistakes.

At the moment, I don't think there's really any HSC subject prerequisites for anything, just 'assumed knowledge'.

It's for 62 degrees at USyd. You can read more about it here: http://smh.com.au/national/education/sydney-university-makes-maths-compulsory-for-62-degrees-20160322-gnp12v.html.

There are probably several factors that contributed to getting rid of it.

They had 4U Science.

On the other thread you were saying to make 3U compulsory, and now you seem to want heaps of people to drop out of it.

Don't think there's HSC prerequisites at the moment, just 'assumed knowledge' (though HSC 2U Maths will be becoming a prerequisite for many degrees at USyd).

If you were referring to resonance, it's not in Preliminary (or HSC) Chemistry.

No

In Riemann sums, the width of rectangles do approach 0, but that doesn't necessarily mean the overall integral is 0, because the number of rectangles used is tending to infinity. Since it says the function is x^j, where j is a positive integer, the answer should be [2^(j+1) – 1]/(j+1), i.e...

Re: University Statistics Discussion Marathon Note that for most practical purposes, something on the order of 10-38 like the Excel calculation there is as good as 0 (since 10-38 = 0.0000…01, where the 1 comes in the 38th decimal place, so there's thirty-seven 0's after the decimal point). The...