I am wassim from Montreal ( student) and I have this problem in an econometrics course
I need to know how to solve the:
As lamda tends to zero, xlamda tends to 1 and hence the numerator and denominator both tend to zero. Thus this problem is a candidate for l'hopital's rule.
My assumption is that your difficulty is differentiating xlamda with respect to lamda. If you don't recall how to differentiate this form ( a constant raised to a variable power) you can proceed as follows.
y'/y = ln(x) and hence y' = y ln(x) = xlamda ln(x).
Now apply l'hopital's rule to your limit and consider the new limit