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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 11.2.4 .
In this activity, we again consider the limit as
\((x,y)\) goes to
\((0,0)\) of
\(g(x,y)=\frac{x^2y^2}{x^2+y^2}\text{,}\) which we previously saw in
Example 11.2.9 .
(a) Convert
\(g\) to polar coordinates.
(b) Find the limit as
\(r\to 0\) of your expression in polar coordinates.
(c) Write a couple of sentences explaining how your answer to the previous part shows that the original limit is
\(0\) and contrast with the previous example.
