Question

Use polar coordinates to find the limit...
\[\lim_{(x,y) \rightarrow (0,0)}(x ^{2}+y ^{2})\ln(x ^{2}+y ^{2})\]

Answer 1

Converting to polar coordinates I got...
\[\lim_{r \rightarrow 0}r ^{2}\ln(r ^{2})\] but ln(0) doesn't exist, so I'm not sure what to do...

Answer 2

now it is single variable...use L'Hospitals rule

Answer 3

Wait, but using L'Hopitals rule...
2r*ln(r^2)+2r

I would still have the ln(0)

Answer 4

\[r^2\ln(r^2)=\frac{\ln(r^2)}{1/r^2}\]

then use L'Hospitals

Answer 5

Alright, I got -r^2, so it would be 0, right?

Answer 6

0 is correct

Answer 7

Thanks!