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z = log ( x^2 + y^2)
Plot3d running on Windows XP with an example of a function that becomes infinite at the origin.
The following images were all created with Plot3d versions 2.0.
z = ( 15 * x^2 * y^2 * exp( -1 * x^2-y^2 ) ) / ( x^2 + y^2 )
Click the image for the larger version.
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z = (sin(x) + cos(y))*sin(x+y)
Point of discontinuity
z = abs( abs(x) - abs(y) ) - abs(x) - abs(y)
Infinity