My textbook describes how some functions are not well approximated by tangent planes at a particular point. For example(adsbygoogle = window.adsbygoogle || []).push({});

f(x)= xy / (x^2 + y^2) for x /= 0

0 for x = 0

at (0,0) the partial derivatives exist and are zero but they are not continuous at 0. What exactly is a 'continuous partial derivative' in two variables? How do you visualize this?

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# Continuous partial derivative?

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