(C^k)–Function

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/C-kFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/C-kFunction.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Code and plots by
Todd Rowland

Plots

<<Utilities`Typesetting`

f3[x_]:=If[x==0,0,x^3 Sin[1/x]];
rescale3[r_]:=Plot[f3[x],{x,-r,r},PlotRange->{{-r,r},{-r^3,r^3}},Ticks->{{-r,0,r},{N[-r^3],N[r^3]}},AspectRatio->1,DisplayFunction->Identity];
plot1=rescale3[1];
plot2=rescale3[.1];
plot3=rescale3[.01];
GraphicsArray[{{plot1,plot2,plot3}},ImageSize->500,PlotLabel->x^3 Sin[InlineFraction[1,x]]]

rescale3[1/100]

Animation

<<Utilities`GIF`

(x^3) sin((x^(-1)))

(*or we could show an animation (warning:this is what crashed my machine using n=100)
*)
Export[gifs<>"ckfn.gif",Show[#,DisplayFunction->$DisplayFunction]&/@Table[rescale3[1/(n)],{n,1,20}]]