# I need help solving a limit

1. Jun 11, 2009

### Ryhion

1. The problem statement, all variables and given/known data

The problem is

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

2. Relevant equations

Consider Log being a logarithm of base 10

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

3. The attempt at a solution

Thanks for all help

2. Jun 11, 2009

### Staff: Mentor

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

3. Jun 12, 2009

### Marksyb

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

4. Jun 12, 2009

### HallsofIvy

Staff Emeritus
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.

5. Jun 12, 2009

### Marksyb

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