# asympt02

Jan 26th, 2015
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1. \begin{asy}
2. // file fodsp.asy
3. //
4. // to get fodsp.pdf, run asy -f pdf fodsp.asy
5. //
6. size(8cm);
7. import graph;
8. import fontsize; defaultpen(fontsize(9pt));
9. texpreamble("\usepackage{lmodern}");
10.
11. pen[] fillpen={
12.   red, orange, yellow, green, lightblue, blue, darkblue
13. };
14.
15. real
16. xmin=0, xmax=20,
17. ymin=0, ymax=20;
18.
19. xaxis(xmin,xmax,RightTicks(Step=10,step=5));
20. yaxis(ymin,ymax, LeftTicks(Step=10,step=5));
21.
22. real ra(real t, real a){return 3*a*sin(t)*cos(t)/(sin(t)^3+cos(t)^3);};
23. real r(real);
24. guide loop;
25.
26. real a, a0=10, da=1;
27. int n=fillpen.length;
28.
29. real t; pair p;
30. a=a0;
31. for(int i=0;i<n;++i){
32.   r=new real(real t){return ra(t,a);};
33.   loop =polargraph(r,0,pi/2)--cycle;
34.   filldraw(loop, 0.7fillpen[i]+0.3white,fillpen[i]);
35.   t=atan(2^(1/3));
36.   p=r(t)*(cos(t),sin(t));
37.   unfill(circle(p,0.7));
38.   label("$"+string(a)+"$",p);
39.   a-=da;
40. }
41.
42. label("$r(\theta)=\displaystyle" 43. +"\frac{3 a \sin\theta\cos\theta}{\sin^3\theta+\cos^3\theta}$, "
44. +"$\theta=[0,\frac\pi2]$, "
45. +"$a="+string(a0-(n-1)*da)+"$--$"+string(a0)+"$"
46. ,((xmin+xmax)/2,ymax),S);
47.
48. shipout(bbox(paleyellow,Fill));
49. \end{asy}