Recent content by 8daysAweek

1. From symmetry, you can assume that alpha >= beta. 2. Now you need to prove that the limit is alpha. 3. Remember the trick where you multiply and then divide by same factor (Think, what factor should it be?).

p is a 2D point. I forgot to mention that d is the distance function between two points. I got this result using the chain rule: \[\frac{{\partial d\left( {{p_i},{p_j}} \right)}}{{\partial {p_i}}} = \frac{{\partial \sqrt {{{\left( {{p_i} - {p_j}} \right)}^2}} }}{{\partial {p_i}}} =...

Homework Statement There are N dogs on the plane. Each dog chases the tail of the next dog with a speed of 1 (and the last dog is chasing the first). I want to prove that the dogs will eventually meet at a single point. 2. The attempt at a solution I defined a function that is sum of...

There is a game with two players: A and B. Each turn the players shoot at each other simultaneously. Player A has 100 life points and the damage he inflicts is 50% of his remaining life points. Player B deals 25% respectively. Life points are rational numbers. A player wins the game when his...

Why do you integrate over a \cdot ln(a)?

Homework Statement f(z) is a complex function that belongs to C^1. Prove that: \lim_{r\to{0}}\frac{1}{r^2}\oint_{\tiny{|z-z_0|=r}}{f(z)dz}=2\pi{i}\frac{\partial f}{\partial \overline z}(z_0) The Attempt at a Solution Using Green's Theorem: \oint_{{C}}{f(z,\overline...

Yes, my mistake, it should be a^2+b^2 without the root. But, still it does not make finding partial derivatives simple. For example, here is du/da calculated by WolframAlpha: Can you explain the real-valued function method? How do you use it as a counter example?

(a,b)=e\Rightarrow{xe=xam+xbn} (1) e | a \Rightarrow{es=a}\Rightarrow{xes=xa}\Rightarrow{xe | xa} (2) e | b \Rightarrow{et=b}\Rightarrow{xet=xb}\Rightarrow{xe | xb} (3) d |xa, d | xb \Rightarrow{di=xa,dj=xb}\Rightarrow{xe=xam+xbn=d(im+jn)}\Rightarrow{d | xe}...

Find all points where the function has a derivative. At which of these points the function is analytical. f(z) = \left\{ \begin{array}{ll} {z^2}sin(\frac{1}{|z^2|}) & z \neq 0 \\ 0 & z = 0} \end{array} \right. I have tried deriving directly using the limit and also tried using...

Homework Statement Solve the following equation: z^4+z^3+z^2+z+1 = 0 z is a complex number. 2. The attempt at a solution I was trying to factorize it to 1st degree polynomial multiplied by 3rd degree polynomial: (z+a)(z^3+bz^2+cz+1/a) = 0 I discovered that I need to solve 3rd...