Math 21a, Fall 2007
Exhibit page Math 21a 07, Multivariable Calculus
Scary: discontinuous f continuous on each line
Course head: Oliver Knill
Office: SciCtr 434
The function
   f(x,y) = x2 y/(x4+y2)
is discontinuous at (0,0) but on each line through the origin, the function is continuous.

The contour map of f. Level curves of different values meet at the origin. The graph of f shows the mountain rist, y=x2 on which the limit is 1/2 On every line through the origin, f is continuous: the limit is 0.
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Math21b | Math 21a | Fall 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University