Question

Find the limit of x^2 * ln (x) as x approaches 0 from the right side. The answer is supposedly 0, but using l'Hospital's rule, I come up with:
lim 2/x which should lead to an infinite limit
x->0

Answer 1

ln(x)/x^(-2)
LH
(1/x)/(-2x^(-3))
=
(-2x^3)/x
=
-2x^2