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