Using L'Hospital's rule with roots and log functions

[fiziksfun]

Can someone help me use L'HOP to determine

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

? I'm confused!

 

[Hootenanny]

Can someone help me use L'HOP to determine

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

? I'm confused!

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.

 

[Dick]

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

 

[Hootenanny]

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

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

 

[fiziksfun]

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

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

 

[cristo]

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

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

 

[Hootenanny]

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

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

 

[cristo]

Edit: Get out of my head cristo