Dirk Bollaerts &
Céleste Paalvast

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Image gallery on the continuity and differentiability of functions of two variables

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Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 1.

Contour plot of a non-differentiable function.

Contour plot of a non-differentiable function. Consult pdf file exercise 2.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 2.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 3.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 7.

Contour plot of a non-differentiable function.

Contour plot of a non-differentiable function. Consult pdf file exercise 9.

Graph plot of a non-continuous function.

Graph plot of a non-continuous function. Consult pdf file exercise 11.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 11.

Graph plot of a non-continuous function.

Graph plot of a non-continuous function. Consult pdf file exercise 12.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 14.

Contour plot of a continuous function.

Contour plot of a continuous function. Consult pdf file exercise 15.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 15.

Contour plot of a continuous function.

Contour plot of a continuous function. Consult pdf file exercise 17.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 24.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 26.

Graph plot of a continuous function.

Graph plot of a continuous function. Consult pdf file exercise 28.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 29.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 31.

Contour plot of a continuous function.

Contour plot of a continuous function. Consult pdf file exercise 31.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 32.

Contour plot of a continuous function.

Contour plot of a continuous function. Consult pdf file exercise 32.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 33.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 33.

Contour plot of a non-differentiable function.

Contour plot of a non-differentiable function. Consult pdf file exercise 33.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 34.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 35.

Contour plot of a differentiable function.

Contour plot of a differentiable function. Consult pdf file exercise 35.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 36.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 37.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 41.

Contour plot of a non-differentiable function.

Contour plot of a non-differentiable function. Consult pdf file exercise 41.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 43.

Contour plot of a differentiable function.

Contour plot of a differentiable function. Consult pdf file exercise 43.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 44.

Contour plot of a differentiable function.

Contour plot of a differentiable function. Consult pdf file exercise 44.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 48.

Contour plot of a non-differentiable function.

Contour plot of a non-differentiable function. Consult pdf file exercise 48.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 49.

Contour plot of an unbounded function.

Contour plot of an unbounded function. Consult pdf file exercise 51.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 51.

Graph plot of a non-continuous function.

Graph plot of a non-continuous function. Consult pdf file exercise 53.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 53.

Graph plot of a continuous non-differentiable function.

Graph plot of a continuous non-differentiable function. Consult pdf file exercise 55.

Contour plot of a continuous non-differentiable function.

Contour plot of a continuous non-differentiable function. Consult pdf file exercise 55.

Graph plot of a non-continuous function.

Graph plot of a non-continuous function. Consult pdf file exercise 61.

Graph plot of a non-continuous function.

Graph plot of a non-continuous function. Consult pdf file exercise 65.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 65.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 66.

Contour plot of a differentiable function.

Contour plot of a differentiable function. Consult pdf file exercise 66.

Graph plot of a differentiable function.

Graph plot of a differentiable function. Consult pdf file exercise 68.

Contour plot of a differentiable function.

Contour plot of a differentiable function. Consult pdf file exercise 68.

Graph plot of a non-differentiable function.

Graph plot of a non-differentiable function. Consult pdf file exercise 69.

Contour plot of a non-differentiable function.

Contour plot of a non-differentiable function. Consult pdf file exercise 69.

Graph plot of a non-continuous function.

Graph plot of a non-continuous function. Consult pdf file exercise 71.

Contour plot of a non-continuous function.

Contour plot of a non-continuous function. Consult pdf file exercise 71.

This website and its pdf texts are copyrighted under the license Creative Commons CC 4.0.

For much more information like function definitions and context, please consider downloading the pdf file. There is also a pdf text with many additional exercises and much more emphasis on the concept of continuity.

If the visitor is interested in showing some of the images for educational purposes, please consider the following advise. The images in this gallery are very reduced in pixel resolution in order to keep the download duration as short as possible. The same images in the pdf file are not reduced in size. The print resolution of those images is about 300 DPI. So they are much more suited for modern printers.