Let (x, y) = xy/(x 2 + y 2 ). Show that (x, y) approaches zero along

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Let ƒ(x, y) = xy/(x2 + y2). Show that ƒ(x, y) approaches zero along the x- and y-axes. Then prove that lim f(x,y) (x,y)(0,0) does not exist by showing that the limit along the line y = x is nonzero.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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