Re: Math help (Because Carrot made me do this)
Graph
y=x(\pi-x)\sin\left(\frac{1}{\sin(x)}\right)
on its largest possible domain inside the interval -\pi\leq x\leq \pi. ;).
Re: Official BOS Mathematics Trial Examinations: Spring Edition.
The limit at the end is just an expression for the derivative of ln(x) at x=1, and the derivative of ln(x) is 1/x...which is 1 at x=1.
Yep, agreed. Glad you are enjoying it! I am doing broad background work in harmonic analysis, functional analysis and PDE theory at the moment.
My proposed thesis problem involves the study of a property known as quantum ergodicity.
Tbh I thought I got full marks raw :P. I felt insanely good about it when I walked out. I checked my answers with other people I knew would be near the top and all my answers where you get a number/algebraic expression at the end were correct. (A couple of these people ranked higher than me). So...
Yep your second method is correct. Incidentally, this is a fantastic bet to make at a party. People who are non-mathematical seem to find it counter-intuitive and when you have say 30 people in the room, the probability jumps to >70%.