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(0,3);
xaxis(0,6);
yaxis(-1,3);
yaxis(-1,2);


real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
real y(real t, real a) { return 2/(1 + a*e^(-3t)); }
real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;
real f(real x) { return y(x,9); }
real f(real x) { return 1 + 1/x; }
real g(real x) { return y(x,-11); }
real g(real x) { return (-1)/x; }
real h(real x) { return y(x,-0.25); }
real h(real x) { return sin(pi * x) * (1/2 + 1/x) + 1/2; }
real j(real x) { return y(x,0); }


draw(graph(f,0,3),red);
draw(graph(f,1,6), dashed);
draw(graph(g,0,0.432),darkgreen); draw(graph(g,1.17,3),darkgreen);
draw(graph(g,1,6), dashed);
draw(graph(h,0,3),blue);
draw(graph(h,0.71,6));
draw(graph(j,0,3),purple);
 
label("$0$",(0,0),W);
label("$K$",(0,2),W);
</asy>
</asy>

Revision as of 04:23, 26 May 2015

[asy] import slopefield;  Label f; f.p=fontsize(6); xaxis(0,6); yaxis(-1,2);  real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286; real f(real x) { return 1 + 1/x; } real g(real x) { return (-1)/x; } real h(real x) { return sin(pi * x) * (1/2 + 1/x) + 1/2; }  draw(graph(f,1,6), dashed); draw(graph(g,1,6), dashed); draw(graph(h,0.71,6)); [/asy]