Série 9

Figure venn.asy

size(0,150);

pen colour1=red;
pen colour2=green;

pair z0=(0,0);
pair z1=(-1,0);
pair z2=(1,0);
real r=1.5;
path c1=circle(z1,r);
path c2=circle(z2,r);
fill(c1,colour1);
fill(c2,colour2);

picture intersection;
fill(intersection,c1,colour1+colour2);
clip(intersection,c2);

add(intersection);

draw(c1);
draw(c2);

label("$A$",z1);
label("$B$",z2);

pair z=(0,-2);
real m=3;
margin BigMargin=Margin(0,m*dot(unit(z1-z),unit(z0-z)));

draw(Label("$A\cap B$",0),conj(z)--z0,Arrow,BigMargin);
draw(Label("$A\cup B$",0),z--z0,Arrow,BigMargin);
draw(z--z1,Arrow,Margin(0,m));
draw(z--z2,Arrow,Margin(0,m));

shipout(bbox(0.25cm));
currentpicture.uptodate=true;

Figure xsin1x.asy

import graph;
size(300,0);

real f(real x) {return (x != 0.0) ? x * sin(1.0 / x) : 0.0;}
pair F(real x) {return (x,f(x));}

xaxis("$x$",red);
yaxis(red);
draw(graph(f,-1.2/pi,1.2/pi,1000));
label("$x\sin\frac{1}{x}$",F(1.1/pi),NW);

picture pic;
size(pic,50,IgnoreAspect);
xaxis(pic,red);
yaxis(pic,red);
draw(pic,graph(pic,f,-0.1/pi,0.1/pi,1000));
attach(bbox(pic,blue),point(N+0.85W),10SE);

Figure yingyang.asy

size(0,25cm);
guide center=(0,1){W}..tension 0.8..(0,0){(1,-.5)}..tension 0.8..{W}(0,-1); 

draw((0,1)..(-1,0)..(0,-1));
filldraw(center{E}..{N}(1,0)..{W}cycle);
unfill(circle((0,0.5),0.125));
fill(circle((0,-0.5),0.125));