Art of Problem Solving

User:5849206328x: Difference between revisions

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<asy>
<asy>
import slopefield;
import slopefield;
real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;


Label f;
Label f;
f.p=fontsize(6);
f.p=fontsize(6);
xaxis(-2,2);
xaxis(0,pi);
yaxis(0,2);
//yaxis(0,2);


real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;
real f(real x, real t) { return 1/(t * sqrt(pi)) * e^(-x^2/t^2); }
real f(real x, real t) { return 1/(t * sqrt(pi)) * e^(-x^2/t^2); }
real f1(real x) { return f(x,1); }
real f1(real x) { return f(x,1); }
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real f3(real x) { return f(x,0.1); }
real f3(real x) { return f(x,0.1); }


draw(graph(f1,-2,2), red + dashed);
dot((0,0)); dot((pi/2,0)); dot((pi,0));
draw(graph(f2,-2,2), blue + dashed);
 
draw(graph(f3,-2,2), darkgreen + dashed);
label("$0$",(0,0),S);
label("$\pi/2$",(pi/2,0),S);
label("$\pi$",(pi,0),S);
 
//draw(graph(f1,-2,2), red + dashed);


limits((-2,0),(2,2),Crop);
//limits((-2,0),(2,2),Crop);
</asy>
</asy>

Revision as of 11:20, 10 June 2015

[asy] import slopefield;  real e  = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286;  Label f; f.p=fontsize(6); xaxis(0,pi); //yaxis(0,2);  real f(real x, real t) { return 1/(t * sqrt(pi)) * e^(-x^2/t^2); } real f1(real x) { return f(x,1); } real f2(real x) { return f(x,0.5); } real f3(real x) { return f(x,0.1); }  dot((0,0)); dot((pi/2,0)); dot((pi,0));  label("$0$",(0,0),S); label("$\pi/2$",(pi/2,0),S); label("$\pi$",(pi,0),S);  //draw(graph(f1,-2,2), red + dashed);  //limits((-2,0),(2,2),Crop); [/asy]