# 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

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+.

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