Showing a Limit Does Not Exist
Multivariable Calculus: Show that the limit(0,0) xy/(x^2 + y^2) does not exist by finding two curves in the xy-plane along which the limit does not agree. We use the curves y=x and y=2x. Failure of the limit is also explained using polar coordinates. For more videos like this one, please visit the Multivariable Calculus playlist at my channel.