l'hospital's rule

[Dorian Gray]

Greetings Mathematicians,

I was wondering if somebody could please give me some guidance on the following problem [ lim as x approaches 0 from the right of (square root of x)(natural log of x) [It is easier to see in my picture). I know that the answer is 0, but I am trying to use l'hospitals rule for the problem. Any comments, thoughts, ideas, and suggestions are always appreciated.

 

[Dorian Gray]

Note: graph does touch y axis but goes no further

 

[Deleted member 4993]

(1/x)/[(-1/2)*x^-3/2] = -2 * x^3/2 * 1/x = -2 * x^1/2

 

[Dorian Gray]

thank you

Thank you! I see what you did

 

[lookagain]

Note: graph does touch y axis but goes no further

\(\displaystyle f(x) \ = \ \sqrt{x}\ln{x}\)


The graph does not touch the y-axis. At x = 0, it is undefined.


The domain is \(\displaystyle (0, \infty).\)

 

[Dorian Gray]

re at lookagain

Ah I see. I must have misread my table. I see what you mea since you cannot have an ln 0