Solving Limit: x.log(x) - Indetermination

[Ryhion]

Homework Statement

The problem is

Limit [x.log(x)]
x->+oo

Homework Equations

Consider Log being a logarithm of base 10

This will tend to +oo, but x.log(x) will become (oo).(oo) which is an indetermination I need to know how to solve the indetermination in this case

The Attempt at a Solution

Thanks for all help

 

[Mark44]

\infty * \infty is NOT an indeterminate form. If you have two quantities that are getting larger and larger, their product will, too. The limit is infinity.

 

[Marksyb]

Bear in mind that
x\log(x) = \frac{\log(x)}{\frac{1}{x}}.
Given that form, you can apply l'Hopital's rule.

 

[HallsofIvy]

No, you can't. That becomes "infinity over 0" which, again, is NOT an "indeterminant". L'Hopilal's rule does not apply and you don't need it.

 

[Marksyb]

No, you can't. That becomes "infinity over 0" which, again, is NOT an "indeterminant". L'Hopilal's rule does not apply and you don't need it.

My apologies; read it too quickly and thought we were talking about a limit as x->0+.