Hopital rule

Question

lim as x tends to 0 ( xlnx) 

 

I know that in order to do hopital rule it has to be in quotient rule. How do I turn xlnx into a fraction ?

Answer 1

x lnx = lnx / (1/x)

 

Now apply L'Hopital's rule.  The derivatives of numerator and denominator give:

 

(1/x) / (-1/x²) = -x²/x = -x

 

So as x → 0, the limit → 0.