I want to calculate limit of $\lim _{\left(x,y\right)\to \left(0,0\right)}\left(\left(xy\right)\ln \left(x^2+y^2\right)\right)$ using Squeeze theorem or using definition of limit. please help
2026-04-24 17:38:09.1777052289
Limit of $\lim _{\left(x,y\right)\to \left(0,0\right)}\left(\left(xy\right)\ln \left(x^2+y^2\right)\right)$
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HINT:
Note that $|xy|\le \frac12(x^2+y^2)$ so that
$$\left|xy\log(x^2+y^2)\right|\le (x^2+y^2)\left|\log\left(\sqrt{x^2+y^2}\right)\right|$$
Can you finish now?