Question

What is limit of x * ln(x) when x approaches 0. Please prove it.

Answer 1

Someone answered
x * ln(x) = ln(x) / (1 / x). Using L'Hospital I get that the limit is 0.
Am I right?

Answer 2

Actually it should be \[\large
\frac{x}{\frac{1}{\ln x}}
\]Because this is an actual indeterminate form.

Answer 3

Look, since \(\ln(x)\) isn't defined for negative values, then the limit can't exist, right?

Answer 4

You can really only do a left hand limit. Is that your goal?