Recent content by Monochrome

Homework Statement f(1)+f(2)...+f(n-1) =< \int_{0}^{n} f(x) dx =< f(2) +f(3)+...+f(n) is increasing and continuous on [1, inf) I'm meat to prove the above, the idea I had was to use the trapezium rule to get an approximation of the integral, but since f''(x) can be either negative or positive...

Homework Statement If C is a n by n matrix with complex coefficient show that there is an integer k >0 that depends only on n such that C, C^2,C^3,...C^k are lin dependent. The Attempt at a Solution Its meant to be a full proof but the only idea I vaguely have is that i^4=i. I'm sure...

:smile: Thanks I forgot that this was dealing with partials. It makes sense now.

Thanks. Just a question: The I after the N is a typo yes? And how did you get d\phi= 0?

Homework Statement M(x,y)y^{'}(x) + N(x,y) = 0 There exists: \phi(x,y) Such that \frac{\partial\phi(x,y)}{\partial x}=N(x,y) \frac{\partial\phi(x,y)}{\partial y}=M(x,y) I'm not looking for a solution to anything particular to this but I can't find the type in my notes and I can't google it...

I'm doing revision for next semesters exams and I ran across this: http://mathworld.wolfram.com/EulerFormula.html Specifically formula no.8. I've seen it before but can't find it in my notes, I forgot what splitting {\frac {d z}{d\theta}} on either side of the equals sign was called. But I...

Extended essay, and beg your coordinator to change. Science ones get low marks and are next to impossible to do when compared to the other subjects, do it in philosophy about science if you must but avoid experiments.

*Hits head on wall* Yes, thanks.

I'm reviewing material for my exams and I came across this: \lim _{x\rightarrow \infty }\sqrt {{x}^{2}+x+1}-\sqrt {{x}^{2}-3\,x} The only explanation it gives is "By the difference of squares" the solution sheet then jumps to: \lim _{x\rightarrow \infty }{\frac {4\,x+1}{\sqrt...

Oh bloody hell, I had that at the start but didn't see the division by d continued to g. Thanks. And about d = 0, the book says we're to assume that d isn't zero, than it just becomes normal division.

I'm working on the proof that two complex numbers can be divided from Alhford and I'm completely s(t)uck. I've gotten as far as: a = gx - dy b = dx +gy from (a+ib) / (g + id) where a+ib = (g + id)(x+iy) I've managed to get x={\frac {b-{\it gy}}{d}} and done the same...

I'd say difficulty wise it goes generally along the lines of : AS level=IB standard/AP/IB higher/A levels. The reason is that most people only ever do 3 A levels for three years.