Art of Problem Solving

User:5849206328x: Difference between revisions

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Label f;
Label f;
f.p=fontsize(6);
f.p=fontsize(6);
xaxis(-1.5,1.5);
// xaxis(-1.5,1.5);
yaxis(-1.5,1.5);
// yaxis(-1.5,1.5);


real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
Line 14: Line 14:
// draw(graph(f,-1.5,1.5,n=10000), red);
// draw(graph(f,-1.5,1.5,n=10000), red);


draw(circle((0,0),1));
label("$a_0b_0$",(0,0));
draw(circle((0,0),0.8),dashed);
label("$a_0b_1$",(1,0));
draw(circle((0,0),1.2),dashed);
label("$a_0b_2$",(2,0));
label("$\cdots$",(3,0));
label("$a_1b_0$",(0,-1));
label("$a_1b_1$",(1,-1));
label("$a_1b_2$",(2,-1));
label("$\cdots$",(3,-1));
label("$a_2b_0$",(0,-2));
label("$a_2b_1$",(1,-2));
label("$a_2b_2$",(2,-2));
label("$\cdots$",(3,-2));
label("$\vdots$",(0,-3));
label("$\vdots$",(1,-3));
label("$\vdots$",(2,-3));
label("$\ddots$",(3,-3));


draw((0,0)--(cos(pi/3),sin(pi/3)));
draw((-0.2,-0.5)--(0.5,-0.5)--(0.5,0.2));
draw((0,0)--(0.4sqrt(2),0.4sqrt(2)),dotted);
draw((-0.2,-1.5)--(1.5,-1.5)--(1.5,0.2));
draw((0,0)--1.2*dir(27),dotted);
draw((-0.2,-2.5)--(2.5,-2.5)--(2.5,0.2));


dot((1/2,1/2));
draw((-0.2,-0.5)--(0.5,0.2),dashed);
dot(1.2*dir(27));
draw((-0.2,-1.5)--(1.5,0.2),dashed);
 
draw((-0.2,-2.5)--(2.5,0.2),dashed);
label("$R$",(1/4,sqrt(3)/4),NW);
draw((0.8,-2.5)--(2.5,-0.8),dashed);
draw((1.8,-2.5)--(2.5,-1.8),dashed);
</asy>
</asy>

Revision as of 09:14, 27 May 2015

[asy] import slopefield;  Label f; f.p=fontsize(6); // xaxis(-1.5,1.5); // yaxis(-1.5,1.5);  real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286; real f(real x) { if (x < 0) return -1; else return 1; } real h(real x) { if (x != 0) return sin(1/x); else return 0; }  // draw(graph(f,-1.5,1.5,n=10000), red);  label("$a_0b_0$",(0,0)); label("$a_0b_1$",(1,0)); label("$a_0b_2$",(2,0)); label("$\cdots$",(3,0)); label("$a_1b_0$",(0,-1)); label("$a_1b_1$",(1,-1)); label("$a_1b_2$",(2,-1)); label("$\cdots$",(3,-1)); label("$a_2b_0$",(0,-2)); label("$a_2b_1$",(1,-2)); label("$a_2b_2$",(2,-2)); label("$\cdots$",(3,-2)); label("$\vdots$",(0,-3)); label("$\vdots$",(1,-3)); label("$\vdots$",(2,-3)); label("$\ddots$",(3,-3));  draw((-0.2,-0.5)--(0.5,-0.5)--(0.5,0.2)); draw((-0.2,-1.5)--(1.5,-1.5)--(1.5,0.2)); draw((-0.2,-2.5)--(2.5,-2.5)--(2.5,0.2));  draw((-0.2,-0.5)--(0.5,0.2),dashed); draw((-0.2,-1.5)--(1.5,0.2),dashed); draw((-0.2,-2.5)--(2.5,0.2),dashed); draw((0.8,-2.5)--(2.5,-0.8),dashed); draw((1.8,-2.5)--(2.5,-1.8),dashed); [/asy]