Homework Statement
Quite a long intro to the question so I thought it easier to include it as an image:
http://img96.imageshack.us/img96/7264/78941753.jpg
http://img686.imageshack.us/img686/7780/39557949.jpg The Attempt at a Solution
I can do Q2.3 and get the payoff matrix given when V=4...
Homework Statement
Consider
f(x)=\sum\frac{1}{n(1+nx^{2})}
from n=1 to n=infinity.
On what intervals of the form (a,b) does the series converge uniformly? On what intervals of the form (a,b) does the series fail to converge uniformly?
Homework Equations
Weierstrass M-test...
Homework Statement
Calculate the outward flux of the two dimensional vector field
f:\Re^{2}\rightarrow\Re^{2} , f(x,y)=(x/2 + y\sqrt{x^{2}+y^{2}},y/2 + x\sqrt{x^{2}+y^{2}})
through the boundary of the ball
\Omega = {(x,y)\in\Re^{2} \left| x^{2}+y^{2} \leq R^{2}} \subset\Re^{2}, R>0...
Yeah I get a similar thing. So we get a turning point of Q at some value t=-psi/phi, and when you put this back into Q you get
\int0 = constant.
Am I being really dumb cos I can't seem to get anything like the inequality from this :((((
Cheers.
Homework Statement
Let
\phi,\psi : [a,b] \rightarrow \Re
be step functions.
Prove that
(\int \phi\psi)^{2} \leq (\int\phi^{2})(\int\psi^{2}) .
Hint: Consider the quadratic function of a real variable t defined by
Q(t)=\int(t\phi+\psi)^2 .
The Attempt at a Solution...
Homework Statement
Let \underline{r} be a regular parameterisation of a space curve C \subset R^{3}. Prove that
\kappa=\frac{\left\|\underline{\dot{r}}\times\underline{\ddot{r}}\right\|}{\left\|\underline{\dot{r}}\right\|^{3}} .
The Attempt at a Solution
We have...
I'm just learning a bit about the "minimal polynomial" today but there was a section from the book which I didn't understand. This is the section, and I've circled the bit I'm having trouble with.
http://img15.imageshack.us/img15/1825/97503873.jpg (sorry, it won't let me post an image for...
Homework Statement
http://img195.imageshack.us/img195/4873/46343978.jpg
The Attempt at a Solution
Part (a) is simple enough, i get
\dot{x}=y
\dot{y}=x^{3}-x.
Equilibrium points occur when the time-derivatives of both x and y are zero, which gives the 3 equilibrium points...
Homework Statement
http://img30.imageshack.us/img30/9954/72990922.jpg
The Attempt at a Solution
I would say the answer to (a) was no but that would be a guess. Does it have to do with the fact that it's done instantaneously, whereas to achieve anything like an irreversible process...
Homework Statement
(a) Use Taylor's theorem with the Lagrange remainder to show that
log(1+x) = \sum^{\infty}_{k=1}\frac{(-1)^{k+1}}{k}x^{k}
for 0<x<1.
(b) Now apply Taylor's theorem to log(1-x) to show that the above result holds for -1<x<0.
Homework Equations
Taylor's...
Oh yeah, hahaha, i always get that wrong!
So we have P = A^{2}e^{-2 \alpha r^{2}}4\pi r^{2}dr then what happens to the dr when i take the derivative? :s
Thanks.