# Homework Help: Using L'Hospital's rule with roots and log functions

1. Oct 7, 2008

### fiziksfun

Can someone help me use L'HOP to determine

lim x -> 0 [ $$\sqrt{x}$$*ln(x) ]

??? I'm confused!!

2. Oct 7, 2008

### Hootenanny

Staff Emeritus
Re: L'hop

L'Hopital's rule doesn't apply here. One can only apply L'Hopital's rule for a limit of a quotient and only then when the limit is undefined.

3. Oct 7, 2008

### Dick

Re: L'hop

Write it as ln(x)/x^(-1/2). Now it's a quotient and infinity/infinity. Looks good for l'hop.

4. Oct 7, 2008

### Hootenanny

Staff Emeritus
Re: L'hop

*Hangs head in shame and shuffles back into the Physics section*

5. Oct 7, 2008

### fiziksfun

Re: L'hop

why can i rewrite x^(1/2) as x^(-1/2) ??? I don't understand.

6. Oct 7, 2008

### cristo

Staff Emeritus
Re: L'hop

You can't, but you can write $$x^{1/2}$$ as $$\frac{1}{x^{-1/2}}$$, which is what Dick has done above.

7. Oct 7, 2008

### Hootenanny

Staff Emeritus
Re: L'hop

You can't rewrite x^(1/2) as x^(-1/2), but you can rewrite it as,

$$x^{1/2} = \frac{1}{x^{-1/2}}$$

as Dick suggests.

Edit: Get out of my head cristo :tongue2:

8. Oct 7, 2008

### cristo

Staff Emeritus
Re: L'hop