Infinite Discontinuity

Author

Eric W. Weisstein
August 25, 2014

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/InfiniteDiscontinuity.nb.

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

©2014 Wolfram Research, Inc. except for portions noted otherwise

Plot

Plot[Piecewise[{{1.1,x==0}},Sin[1/x]],{x,-1,1},LabelStyle->{Black,FontFamily->"Times"},PlotStyle->Red,PlotRangeClipping->False,Epilog->{Red,PointSize[0.0125],Point[{0,1.1}]},AxesLabel->{x,y},PlotLabel->f[x,y]]

Tan

GraphicsRow[{
Plot[Tan[x],{x,-2π,2π},Exclusions->Table[n Pi/2,{n,-3,3,2}],LabelStyle->{Black,FontFamily->"Times"},PlotStyle->Red,Epilog->{Blue,Dashing[.02],Line[Table[{{n Pi/2,-7},{n Pi/2,7}},{n,-3,3,2}]]},PlotLabel->Tan[x]],
Plot3D[Re[Tan[x+I y]],{x,-3,3},{y,-3,3},ClippingStyle->None,LabelStyle->{Black,FontFamily->"Times"},PlotLabel->Re[Tan[z]]],
Plot3D[Im[Tan[x+I y]],{x,-3,3},{y,-3,3},ClippingStyle->None,LabelStyle->{Black,FontFamily->"Times"},PlotLabel->Im[Tan[z]]]
},ImageSize->400]